Finite Group Databasebeta

← C73×#26754 #32936158

Subgroups — C73×#26754 #32936158

Order 18688.

812 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2507C211yesmaximal, characteristic, complemented
2C73×#2366C211yesmaximal, characteristic
3C73×#2071C211yesmaximal, characteristic, complemented
4C73×#2065C211yesmaximal, characteristic, complemented
5C73×#2041C211yesmaximal, characteristic
6C73×#2041C211yesmaximal, characteristic
7C73×#1934C211yesmaximal, characteristic, complemented
8C73×#1926C211yesmaximal, characteristic, complemented
9C73×#1920C211yesmaximal, characteristic, complemented
10C73×#1920C211yesmaximal, characteristic, complemented
11C73×#1916C211yesmaximal, characteristic, complemented
12C73×#1864C211yesmaximal, characteristic, complemented
13C73×#1864C211yesmaximal, characteristic, complemented
14C73×#1802C211yesmaximal, characteristic, complemented
15C4×#102×C73C211yesmaximal, characteristic, complemented
16C2×#127×C73C2211yescharacteristic
17C2×C4×D4×C73—21no—
18C2×C4×D4×C73C2211yescharacteristic
19C2×C4×D4×C73C2211yescharacteristic
20C2×#106×C73C2211yescharacteristic
21C2×#106×C73C2211yescharacteristic
22C2×C4⋊C8×C73C2211yescharacteristic
23C2×#102×C73C2211yescharacteristic
24C2×#102×C73C2211yescharacteristic
25C2×#102×C73C2211yescharacteristic
26C2×#102×C73C2211yescharacteristic
27C2×#102×C73C2211yescharacteristic
28C2×#102×C73C2211yescharacteristic
29C2×#102×C73C2211yescharacteristic
30C2×#102×C73C2211yescharacteristic
31C2×C4×C8×C73C2211yescharacteristic
32#398×C73—21no—
33#398×C73—21no—
34#390×C73—21no—
35#390×C73C2211yescharacteristic
36#390×C73C2211yescharacteristic
37#389×C73—21no—
38#389×C73C2211yescharacteristic
39#389×C73C2211yescharacteristic
40#389×C73C2211yescharacteristic
41#389×C73C2211yescharacteristic
42#387×C73—21no—
43#386×C73—21no—
44#386×C73—21no—
45#384×C73C2211yescharacteristic
46C4×C4⋊C4×C73C2211yescharacteristic
47C4×C4⋊C4×C73C2211yescharacteristic
48C4×C4⋊C4×C73C2211yescharacteristic
49#340×C73C2211yescharacteristic
50#340×C73C2211yescharacteristic
51#340×C73C2211yescharacteristic
52#340×C73C2211yescharacteristic
53#340×C73C2211yescharacteristic
54#340×C73C2211yescharacteristic
55#336×C73C2211yescharacteristic
56#336×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×D4×C73—21no—
60C22×D4×C73—21no—
61C22×D4×C73C2311yescharacteristic
62C22×D4×C73C2311yescharacteristic
63C23×C4×C73—21no—
64C23×C4×C73—21no—
65C22×C8×C73C2311yescharacteristic
66C22×C8×C73C2311yescharacteristic
67C22×C8×C73C2311yescharacteristic
68C22×C8×C73C2311yescharacteristic
69#127×C73—22no—
70#127×C73—22no—
71C4×D4×C73—22no—
72C4×D4×C73—22no—
73C4×D4×C73—41no—
74C4×D4×C73—41no—
75C4×D4×C73—44no—
76C2×C4⋊C4×C73—21no—
77C2×C4⋊C4×C73—21no—
78C2×C4⋊C4×C73—21no—
79C2×C4⋊C4×C73—21no—
80C2×C4⋊C4×C73—21no—
81C2×C4⋊C4×C73—21no—
82C2×C4⋊C4×C73D411yescharacteristic
83C2×C4⋊C4×C73D411yescharacteristic
84C2×C4⋊C4×C73C2311yescharacteristic
85C2×C4⋊C4×C73C2311yescharacteristic
86C2×C4⋊C4×C73C2311yescharacteristic
87C2×C4⋊C4×C73C2311yescharacteristic
88C2×C4⋊C4×C73C2311yescharacteristic
89C2×C4⋊C4×C73C2311yescharacteristic
90C2×C22⋊C4×C73—21no—
91C2×C22⋊C4×C73—21no—
92C2×C22⋊C4×C73—21no—
93C2×C22⋊C4×C73—21no—
94C2×C22⋊C4×C73—21no—
95C2×C22⋊C4×C73—21no—
96C2×C42×C73—21no—
97C2×C42×C73—21no—
98C2×C42×C73C2311yescharacteristic
99C2×C42×C73C2311yescharacteristic
100C2×C42×C73C2311yescharacteristic
101#106×C73—22no—
102#106×C73—22no—
103C4⋊C8×C73—41no—
104#102×C73—22no—
105#102×C73—22no—
106#102×C73—22no—
107#102×C73—22no—
108#102×C73—22no—
109#102×C73—22no—
110#102×C73—41no—
111#102×C73—41no—
112C4×C8×C73—41no—
113#95×C73—21no—
114#95×C73—21no—
115#95×C73—21no—
116#95×C73—21no—
117#95×C73—21no—
118#95×C73—21no—
119#95×C73D411yescharacteristic
120#95×C73D411yescharacteristic
121C24×C73—21no—
122C24×C73—21no—
123C2×D4×C73—24no—
124C2×D4×C73—24no—
125C2×D4×C73—21no—
126C2×D4×C73—21no—
127C2×D4×C73—21no—
128C2×D4×C73—21no—
129C2×D4×C73—21no—
130C2×D4×C73—21no—
131C2×D4×C73—21no—
132C2×D4×C73—21no—
133C2×D4×C73—21no—
134C2×D4×C73—21no—
135C2×D4×C73—42no—
136C2×D4×C73—42no—
137C2×D4×C73—81no—
138C2×D4×C73—81no—
139C2×D4×C73#4112yes—
140C2×D4×C73#4112yes—
141C22×C4×C73—21no—
142C22×C4×C73—21no—
143C22×C4×C73—21no—
144C22×C4×C73—21no—
145C22×C4×C73—21no—
146C22×C4×C73—21no—
147C22×C4×C73—42no—
148C22×C4×C73—42no—
149C22×C4×C73—42no—
150C22×C4×C73—42no—
151C22×C4×C73—81no—
152C22×C4×C73—81no—
153C22×C4×C73C2×D411yescharacteristic
154C22×C4×C73C2×D411yescharacteristic
155C22×C4×C73C2×D411yescharacteristic
156C22×C4×C73C2×D411yescharacteristic
157C22×C4×C73C2×D411yescharacteristic
158C22×C4×C73C2×D411yescharacteristic
159C22×C4×C73C2411yescharacteristic
160C2×C8×C73—21no—
161C2×C8×C73—21no—
162C2×C8×C73—21no—
163C2×C8×C73—21no—
164C2×C8×C73—21no—
165C2×C8×C73—21no—
166C2×C8×C73—21no—
167C2×C8×C73—21no—
168C2×C8×C73—21no—
169C2×C8×C73—21no—
170C2×C8×C73—21no—
171C2×C8×C73—21no—
172C4⋊C4×C73—21no—
173C4⋊C4×C73—21no—
174C4⋊C4×C73—21no—
175C4⋊C4×C73—21no—
176C4⋊C4×C73—21no—
177C4⋊C4×C73—21no—
178C4⋊C4×C73—21no—
179C4⋊C4×C73—21no—
180C4⋊C4×C73—21no—
181C4⋊C4×C73—21no—
182C4⋊C4×C73—41no—
183C4⋊C4×C73—42no—
184C4⋊C4×C73—81no—
185C4⋊C4×C73—81no—
186C4⋊C4×C73—81no—
187C4⋊C4×C73—81no—
188C4⋊C4×C73—81no—
189C4⋊C4×C73SD1614yes—
190C4⋊C4×C73#4112yes—
191C4⋊C4×C73#4112yes—
192C22⋊C4×C73—42no—
193C22⋊C4×C73—42no—
194C22⋊C4×C73—42no—
195C22⋊C4×C73—42no—
196C22⋊C4×C73—81no—
197C22⋊C4×C73—81no—
198C42×C73—21no—
199C42×C73—21no—
200C42×C73—21no—
201C42×C73—21no—
202C42×C73—21no—
203C42×C73—21no—
204C42×C73—42no—
205C42×C73—81no—
206C23×C73—22no—
207C23×C73—22no—
208C23×C73—41no—
209C23×C73—41no—
210C23×C73—41no—
211C23×C73—41no—
212C23×C73—41no—
213C23×C73—41no—
214C23×C73—41no—
215C23×C73—41no—
216C23×C73—41no—
217C23×C73—41no—
218C23×C73—41no—
219C23×C73—41no—
220C23×C73C22×D411yescharacteristic
221D4×C73—22no—
222D4×C73—22no—
223D4×C73—22no—
224D4×C73—22no—
225D4×C73—48no—
226D4×C73—41no—
227D4×C73—41no—
228D4×C73—41no—
229D4×C73—41no—
230D4×C73—84no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—21no—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—22no—
241C2×C4×C73—22no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—21no—
248C2×C4×C73—41no—
249C2×C4×C73—41no—
250C2×C4×C73—41no—
251C2×C4×C73—41no—
252C2×C4×C73—41no—
253C2×C4×C73—41no—
254C2×C4×C73—41no—
255C2×C4×C73—41no—
256C2×C4×C73—41no—
257C2×C4×C73—41no—
258C2×C4×C73—41no—
259C2×C4×C73—41no—
260C2×C4×C73—41no—
261C2×C4×C73—41no—
262C2×C4×C73—41no—
263C2×C4×C73—41no—
264C2×C4×C73—84no—
265C2×C4×C73—84no—
266C2×C4×C73C2×SD1612yes—
267C2×C4×C73C2×SD1612yes—
268C2×C4×C73C2×SD1612yes—
269C2×C4×C73C2×#4111yescharacteristic
270C2×C4×C73C2×#4111yescharacteristic
271C2×C4×C73C2×#4111yescharacteristic
272C2×C4×C73C2×#4111yescharacteristic
273C2×C4×C73H(5,𝔽2)11yescharacteristic
274C2×C4×C732−1+411yescharacteristic
275C8×C73—41no—
276C8×C73—41no—
277C8×C73—41no—
278C8×C73—41no—
279C22×C73—42no—
280C22×C73—42no—
281C22×C73—42no—
282C22×C73—42no—
283C22×C73—42no—
284C22×C73—42no—
285C22×C73—81no—
286C22×C73—81no—
287C22×C73—81no—
288C22×C73—81no—
289C22×C73—81no—
290C22×C73—81no—
291C22×C73—81no—
292C22×C73—81no—
293C22×C73#52511yescharacteristic
294C22×C73#54611yescharacteristic
295C22×C73#54811yescharacteristic
296C22×C73C22×SD1611yescharacteristic
297C22×C73#57511yescharacteristic
298C22×C73#57611yescharacteristic
299C22×C73#57611yescharacteristic
300C4×C73—22no—
301C4×C73—22no—
302C4×C73—22no—
303C4×C73—42no—
304C4×C73—41no—
305C4×C73—42no—
306C4×C73—41no—
307C4×C73—41no—
308C4×C73—81no—
309C4×C73—81no—
310C4×C73—81no—
311C4×C73—81no—
312C4×C73#52911yescharacteristic
313C4×C73#53911yescharacteristic
314C4×C73#55211yescharacteristic
315C4×C73#55311yescharacteristic
316#26754C7311yesmaximal, characteristic, direct product factor, Sylow
317C2×C73—82no—
318C2×C73—82no—
319C2×C73#246011yescharacteristic
320C2×C73#310111yescharacteristic
321C2×C73#312211yescharacteristic
322C2×C73#329511yescharacteristic
323C2×C73#330911yescharacteristic
324C2×C73#336211yescharacteristic
325C2×C73#337011yescharacteristic
326#2507C2×C7311yescharacteristic, complemented
327#2366C2×C7311yescharacteristic
328#2071C2×C7311yescharacteristic, complemented
329#2065C2×C7311yescharacteristic, complemented
330#2041C2×C7311yescharacteristic
331#2041C2×C7311yescharacteristic
332#1934C2×C7311yescharacteristic, complemented
333#1926C2×C7311yescharacteristic, complemented
334#1920C2×C7311yescharacteristic, complemented
335#1920C2×C7311yescharacteristic, complemented
336#1916C2×C7311yescharacteristic, complemented
337#1864C2×C7311yescharacteristic, complemented
338#1864C2×C7311yescharacteristic, complemented
339#1802C2×C7311yescharacteristic, complemented
340C4×#102C2×C7311yescharacteristic, complemented
341C73#2675411yescharacteristic, direct product factor, Sylow
342C2×#127C22×C7311yescharacteristic
343C2×C4×D4—21no—
344C2×C4×D4C22×C7311yescharacteristic
345C2×C4×D4C22×C7311yescharacteristic
346C2×#106C22×C7311yescharacteristic
347C2×#106C22×C7311yescharacteristic
348C2×C4⋊C8C22×C7311yescharacteristic
349C2×#102C22×C7311yescharacteristic
350C2×#102C22×C7311yescharacteristic
351C2×#102C22×C7311yescharacteristic
352C2×#102C22×C7311yescharacteristic
353C2×#102C22×C7311yescharacteristic
354C2×#102C22×C7311yescharacteristic
355C2×#102C22×C7311yescharacteristic
356C2×#102C22×C7311yescharacteristic
357C2×C4×C8C22×C7311yescharacteristic
358#398—21no—
359#398—21no—
360#390—21no—
361#390C22×C7311yescharacteristic
362#390C22×C7311yescharacteristic
363#389—21no—
364#389C22×C7311yescharacteristic
365#389C22×C7311yescharacteristic
366#389C22×C7311yescharacteristic
367#389C22×C7311yescharacteristic
368#387—21no—
369#386—21no—
370#386—21no—
371#384C22×C7311yescharacteristic
372C4×C4⋊C4C22×C7311yescharacteristic
373C4×C4⋊C4C22×C7311yescharacteristic
374C4×C4⋊C4C22×C7311yescharacteristic
375#340C22×C7311yescharacteristic
376#340C22×C7311yescharacteristic
377#340C22×C7311yescharacteristic
378#340C22×C7311yescharacteristic
379#340C22×C7311yescharacteristic
380#340C22×C7311yescharacteristic
381#336C22×C7311yescharacteristic
382#336C22×C7311yescharacteristic
383#336C22×C7311yescharacteristic
384#336C22×C7311yescharacteristic
385C22×D4—21no—
386C22×D4—21no—
387C22×D4C23×C7311yescharacteristic
388C22×D4C23×C7311yescharacteristic
389C23×C4—21no—
390C23×C4—21no—
391C22×C8C23×C7311yescharacteristic
392C22×C8C23×C7311yescharacteristic
393C22×C8C23×C7311yescharacteristic
394C22×C8C23×C7311yescharacteristic
395#127—22no—
396#127—22no—
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—41no—
400C4×D4—41no—
401C4×D4—44no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4D4×C7311yescharacteristic
409C2×C4⋊C4D4×C7311yescharacteristic
410C2×C4⋊C4C23×C7311yescharacteristic
411C2×C4⋊C4C23×C7311yescharacteristic
412C2×C4⋊C4C23×C7311yescharacteristic
413C2×C4⋊C4C23×C7311yescharacteristic
414C2×C4⋊C4C23×C7311yescharacteristic
415C2×C4⋊C4C23×C7311yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42C23×C7311yescharacteristic
425C2×C42C23×C7311yescharacteristic
426C2×C42C23×C7311yescharacteristic
427#106—22no—
428#106—22no—
429C4⋊C8—41no—
430#102—22no—
431#102—22no—
432#102—22no—
433#102—22no—
434#102—22no—
435#102—22no—
436#102—41no—
437#102—41no—
438C4×C8—41no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95D4×C7311yescharacteristic
446#95D4×C7311yescharacteristic
447C24—21no—
448C24—21no—
449C2×D4—24no—
450C2×D4—24no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—81no—
464C2×D4—81no—
465C2×D4#41×C7312yes—
466C2×D4#41×C7312yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—81no—
478C22×C4—81no—
479C22×C4C2×D4×C7311yescharacteristic
480C22×C4C2×D4×C7311yescharacteristic
481C22×C4C2×D4×C7311yescharacteristic
482C22×C4C2×D4×C7311yescharacteristic
483C22×C4C2×D4×C7311yescharacteristic
484C22×C4C2×D4×C7311yescharacteristic
485C22×C4C24×C7311yescharacteristic
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—41no—
509C4⋊C4—42no—
510C4⋊C4—81no—
511C4⋊C4—81no—
512C4⋊C4—81no—
513C4⋊C4—81no—
514C4⋊C4—81no—
515C4⋊C4SD16×C7314yes—
516C4⋊C4#41×C7312yes—
517C4⋊C4#41×C7312yes—
518C22⋊C4—42no—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—81no—
523C22⋊C4—81no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—42no—
531C42—81no—
532C23—22no—
533C23—22no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23C22×D4×C7311yescharacteristic
547D4—22no—
548D4—22no—
549D4—22no—
550D4—22no—
551D4—48no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—84no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—84no—
591C2×C4—84no—
592C2×C4C2×SD16×C7312yes—
593C2×C4C2×SD16×C7312yes—
594C2×C4C2×SD16×C7312yes—
595C2×C4C2×#41×C7311yescharacteristic
596C2×C4C2×#41×C7311yescharacteristic
597C2×C4C2×#41×C7311yescharacteristic
598C2×C4C2×#41×C7311yescharacteristic
599C2×C4H(5,𝔽2)×C7311yescharacteristic
600C2×C42−1+4×C7311yescharacteristic
601C8—41no—
602C8—41no—
603C8—41no—
604C8—41no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22#525×C7311yescharacteristic
620C22#546×C7311yescharacteristic
621C22#548×C7311yescharacteristic
622C22C22×SD16×C7311yescharacteristic
623C22#575×C7311yescharacteristic
624C22#576×C7311yescharacteristic
625C22#576×C7311yescharacteristic
626C4—22no—
627C4—22no—
628C4—22no—
629C4—42no—
630C4—41no—
631C4—41no—
632C4—42no—
633C4—41no—
634C4—81no—
635C4—81no—
636C4—81no—
637C4—81no—
638C4#529×C7311yescharacteristic
639C4#539×C7311yescharacteristic
640C4#552×C7311yescharacteristic
641C4#553×C7311yescharacteristic
642C2—82no—
643C2—82no—
644C2C73×#246011yescharacteristic
645C2C73×#310111yescharacteristic
646C2C73×#312211yescharacteristic
647C2C73×#329511yescharacteristic
648C2C73×#330911yescharacteristic
649C2C73×#336211yescharacteristic
650C2C73×#337011yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#127×C73C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C4⋊C4×C73 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C73×#2507C2semidirect
3. C73×#2071C2semidirect
4. C73×#2065C2semidirect
7. C73×#1934C2semidirect
8. C73×#1926C2semidirect
9. C73×#1920C2semidirect
10. C73×#1920C2semidirect
11. C73×#1916C2semidirect
12. C73×#1864C2semidirect
13. C73×#1864C2semidirect
14. C73×#1802C2semidirect
15. C4×#102×C73C2semidirect
316. #26754C73direct (N × H)
326. #2507C2×C73semidirect
328. #2071C2×C73semidirect
329. #2065C2×C73semidirect
332. #1934C2×C73semidirect
333. #1926C2×C73semidirect
334. #1920C2×C73semidirect
335. #1920C2×C73semidirect
336. #1916C2×C73semidirect
337. #1864C2×C73semidirect
338. #1864C2×C73semidirect
339. #1802C2×C73semidirect
340. C4×#102C2×C73semidirect
341. C73#26754direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C73×#25072
C73×#23662
C73×#20712
C73×#20652
C73×#20412
C73×#19342
C73×#19262
C73×#19202
C73×#19162
C73×#18642
C73×#18022
C4×#102×C732
#2675473