Finite Group Databasebeta

← C73×#14870 #32924274

Subgroups — C73×#14870 #32924274

Order 18688.

1638 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#399×C73C211yesmaximal, characteristic
2C2×#398×C73C212yesmaximal, complemented
3C2×#396×C73C212yesmaximal
4C2×#389×C73C211yesmaximal, characteristic, complemented
5C2×#388×C73C211yesmaximal, characteristic
6C2×C4×C4⋊C4×C73C211yesmaximal, characteristic, complemented
7C73×#1445C211yesmaximal, characteristic, complemented
8C73×#1444C211yesmaximal, characteristic, complemented
9C73×#1439C211yesmaximal, characteristic
10C73×#1437C212yesmaximal
11C73×C4⋊#95C212yesmaximal, complemented
12C22×C4⋊C4×C73C2212yes—
13C22×C4⋊C4×C73C2211yescharacteristic
14C22×C4⋊C4×C73C2211yescharacteristic
15C22×C4⋊C4×C73C2211yescharacteristic
16C22×C4⋊C4×C73C2212yes—
17C22×C4⋊C4×C73C2212yes—
18C22×C4⋊C4×C73C2212yes—
19C22×C22⋊C4×C73C2212yes—
20C22×C22⋊C4×C73C2211yescharacteristic
21C22×C22⋊C4×C73C2211yescharacteristic
22C22×C22⋊C4×C73C2212yes—
23C22×C22⋊C4×C73C2211yescharacteristic
24C22×C42×C73C2212yes—
25C22×C42×C73C2211yescharacteristic
26#399×C73—24no—
27#398×C73—28no—
28#396×C73—28no—
29#389×C73—24no—
30#388×C73—24no—
31C4×C4⋊C4×C73—24no—
32C2×#95×C73C2211yescharacteristic
33C2×#95×C73C2212yes—
34C2×#95×C73C2212yes—
35C2×#95×C73C2212yes—
36C2×#95×C73C2212yes—
37C2×#95×C73C2212yes—
38C2×#95×C73C2211yescharacteristic
39C2×#95×C73C2211yescharacteristic
40C2×#95×C73C2211yescharacteristic
41C25×C73C2311yescharacteristic
42C23×C4×C73C2312yes—
43C23×C4×C73C2311yescharacteristic
44C23×C4×C73C2311yescharacteristic
45C23×C4×C73C2312yes—
46C23×C4×C73C2311yescharacteristic
47C23×C4×C73C2312yes—
48C23×C4×C73C2311yescharacteristic
49C23×C4×C73C2312yes—
50C23×C4×C73C2311yescharacteristic
51C23×C4×C73C2311yescharacteristic
52C2×C4⋊C4×C73—24no—
53C2×C4⋊C4×C73—22no—
54C2×C4⋊C4×C73—24no—
55C2×C4⋊C4×C73—24no—
56C2×C4⋊C4×C73—22no—
57C2×C4⋊C4×C73—22no—
58C2×C4⋊C4×C73—24no—
59C2×C4⋊C4×C73—24no—
60C2×C4⋊C4×C73—24no—
61C2×C4⋊C4×C73—24no—
62C2×C4⋊C4×C73—24no—
63C2×C4⋊C4×C73—24no—
64C2×C4⋊C4×C73—22no—
65C2×C4⋊C4×C73—24no—
66C2×C4⋊C4×C73—24no—
67C2×C4⋊C4×C73—22no—
68C2×C4⋊C4×C73—24no—
69C2×C4⋊C4×C73—42no—
70C2×C4⋊C4×C73D418yes—
71C2×C22⋊C4×C73—22no—
72C2×C22⋊C4×C73—22no—
73C2×C22⋊C4×C73—22no—
74C2×C22⋊C4×C73—22no—
75C2×C22⋊C4×C73—24no—
76C2×C22⋊C4×C73—24no—
77C2×C22⋊C4×C73—24no—
78C2×C22⋊C4×C73—22no—
79C2×C22⋊C4×C73—24no—
80C2×C22⋊C4×C73—24no—
81C2×C22⋊C4×C73—22no—
82C2×C22⋊C4×C73—24no—
83C2×C22⋊C4×C73—42no—
84C2×C22⋊C4×C73Q814yes—
85C2×C42×C73—22no—
86C2×C42×C73—22no—
87C2×C42×C73—24no—
88C2×C42×C73—24no—
89C2×C42×C73—42no—
90C2×C42×C73D414yes—
91#95×C73—22no—
92#95×C73—22no—
93#95×C73—22no—
94#95×C73—24no—
95#95×C73—24no—
96#95×C73—24no—
97#95×C73—24no—
98#95×C73—24no—
99#95×C73D414yes—
100C24×C73—21no—
101C24×C73—21no—
102C24×C73—22no—
103C24×C73—21no—
104C24×C73—22no—
105C24×C73—22no—
106C24×C73—21no—
107C24×C73—21no—
108C24×C73—22no—
109C24×C73—21no—
110C24×C73C2×Q812yes—
111C24×C73C2411yescharacteristic
112C22×C4×C73—21no—
113C22×C4×C73—21no—
114C22×C4×C73—21no—
115C22×C4×C73—21no—
116C22×C4×C73—22no—
117C22×C4×C73—22no—
118C22×C4×C73—22no—
119C22×C4×C73—22no—
120C22×C4×C73—21no—
121C22×C4×C73—22no—
122C22×C4×C73—22no—
123C22×C4×C73—21no—
124C22×C4×C73—22no—
125C22×C4×C73—22no—
126C22×C4×C73—22no—
127C22×C4×C73—22no—
128C22×C4×C73—21no—
129C22×C4×C73—22no—
130C22×C4×C73—22no—
131C22×C4×C73—22no—
132C22×C4×C73—21no—
133C22×C4×C73—22no—
134C22×C4×C73—22no—
135C22×C4×C73—22no—
136C22×C4×C73—22no—
137C22×C4×C73—22no—
138C22×C4×C73—22no—
139C22×C4×C73—22no—
140C22×C4×C73—22no—
141C22×C4×C73—21no—
142C22×C4×C73—21no—
143C22×C4×C73—22no—
144C22×C4×C73—22no—
145C22×C4×C73—22no—
146C22×C4×C73—22no—
147C22×C4×C73—22no—
148C22×C4×C73—21no—
149C22×C4×C73—22no—
150C22×C4×C73—22no—
151C22×C4×C73—21no—
152C22×C4×C73—22no—
153C22×C4×C73—22no—
154C22×C4×C73—22no—
155C22×C4×C73—22no—
156C22×C4×C73—21no—
157C22×C4×C73—21no—
158C22×C4×C73C2×D414yes—
159C22×C4×C73C2×D412yes—
160C22×C4×C73C2×D412yes—
161C22×C4×C73C2×D414yes—
162C22×C4×C73C2×D414yes—
163C22×C4×C73C2×D412yes—
164C22×C4×C73C2×D412yes—
165C22×C4×C73C2×D414yes—
166C22×C4×C73C2×Q812yes—
167C22×C4×C73C2×Q812yes—
168C22×C4×C73#4114yes—
169C22×C4×C73#4112yes—
170C22×C4×C73#4114yes—
171C22×C4×C73#4112yes—
172C4⋊C4×C73—28no—
173C4⋊C4×C73—216no—
174C4⋊C4×C73—48no—
175C4⋊C4×C73—44no—
176C4⋊C4×C73—48no—
177C4⋊C4×C73—44no—
178C4⋊C4×C73—48no—
179C22⋊C4×C73—28no—
180C22⋊C4×C73—48no—
181C22⋊C4×C73—44no—
182C22⋊C4×C73—48no—
183C22⋊C4×C73—44no—
184C42×C73—28no—
185C42×C73—48no—
186C23×C73—22no—
187C23×C73—24no—
188C23×C73—22no—
189C23×C73—24no—
190C23×C73—22no—
191C23×C73—41no—
192C23×C73—42no—
193C23×C73—41no—
194C23×C73—42no—
195C23×C73—41no—
196C23×C73—41no—
197C23×C73—42no—
198C23×C73—41no—
199C23×C73—41no—
200C23×C73—42no—
201C23×C73—42no—
202C23×C73—42no—
203C23×C73—41no—
204C23×C73—42no—
205C23×C73—42no—
206C23×C73—42no—
207C23×C73—41no—
208C23×C73—42no—
209C23×C73C22×D411yescharacteristic
210C23×C73C22×D411yescharacteristic
211C23×C73C22×D412yes—
212C23×C73C22×Q811yescharacteristic
213C23×C73C2×#4112yes—
214C23×C73C2×#4111yescharacteristic
215C23×C73C2×#4111yescharacteristic
216C23×C73C2×#4112yes—
217C23×C73H(5,𝔽2)11yescharacteristic
218C23×C732−1+412yes—
219C23×C732−1+411yescharacteristic
220C2×C4×C73—22no—
221C2×C4×C73—22no—
222C2×C4×C73—24no—
223C2×C4×C73—22no—
224C2×C4×C73—24no—
225C2×C4×C73—22no—
226C2×C4×C73—24no—
227C2×C4×C73—22no—
228C2×C4×C73—22no—
229C2×C4×C73—24no—
230C2×C4×C73—22no—
231C2×C4×C73—24no—
232C2×C4×C73—24no—
233C2×C4×C73—24no—
234C2×C4×C73—24no—
235C2×C4×C73—24no—
236C2×C4×C73—22no—
237C2×C4×C73—24no—
238C2×C4×C73—22no—
239C2×C4×C73—22no—
240C2×C4×C73—24no—
241C2×C4×C73—22no—
242C2×C4×C73—24no—
243C2×C4×C73—24no—
244C2×C4×C73—24no—
245C2×C4×C73—24no—
246C2×C4×C73—24no—
247C2×C4×C73—24no—
248C2×C4×C73—42no—
249C2×C4×C73—42no—
250C2×C4×C73—41no—
251C2×C4×C73—41no—
252C2×C4×C73—42no—
253C2×C4×C73—42no—
254C2×C4×C73—42no—
255C2×C4×C73—42no—
256C2×C4×C73—42no—
257C2×C4×C73—42no—
258C2×C4×C73—42no—
259C2×C4×C73—41no—
260C2×C4×C73—42no—
261C2×C4×C73—42no—
262C2×C4×C73—42no—
263C2×C4×C73—42no—
264C2×C4×C73—41no—
265C2×C4×C73—41no—
266C2×C4×C73—41no—
267C2×C4×C73—42no—
268C2×C4×C73—41no—
269C2×C4×C73—42no—
270C2×C4×C73—42no—
271C2×C4×C73—42no—
272C2×C4×C73—42no—
273C2×C4×C73—41no—
274C2×C4×C73—42no—
275C2×C4×C73—42no—
276C2×C4×C73#12114yes—
277C2×C4×C73#12118yes—
278C2×C4×C73C22⋊Q814yes—
279C2×C4×C73#12714yes—
280C22×C73—42no—
281C22×C73—42no—
282C22×C73—44no—
283C22×C73—42no—
284C22×C73—44no—
285C22×C73—81no—
286C22×C73—81no—
287C22×C73—81no—
288C22×C73—82no—
289C22×C73—82no—
290C22×C73—81no—
291C22×C73C2×#12111yescharacteristic
292C22×C73C2×#12112yes—
293C22×C73C2×C22⋊Q811yescharacteristic
294C22×C73#52511yescharacteristic
295C22×C73#52912yes—
296C22×C73C2×#12711yescharacteristic
297C22×C73#53211yescharacteristic
298C22×C73#53212yes—
299C22×C73#53312yes—
300C22×C73#53611yescharacteristic
301C22×C73#53711yescharacteristic
302C22×C73#53912yes—
303C22×C73#54112yes—
304C22×C73#54611yescharacteristic
305C22×C73#54612yes—
306C22×C73#54712yes—
307C22×C73#54712yes—
308C22×C73#54812yes—
309C22×C73D4×Q811yescharacteristic
310C22×C73D4×Q812yes—
311C22×C73#55212yes—
312C22×C73#55211yescharacteristic
313C22×C73#55411yescharacteristic
314C4×C73—24no—
315C4×C73—24no—
316C4×C73—24no—
317C4×C73—28no—
318C4×C73—44no—
319C4×C73—44no—
320C4×C73—42no—
321C4×C73—81no—
322C4×C73—82no—
323C4×C73—81no—
324#14870C7311yesmaximal, characteristic, direct product factor, Sylow
325C2×C73—82no—
326C2×C73#239611yescharacteristic
327C2×C73#241311yescharacteristic
328C2×C73#241711yescharacteristic
329C2×C73#242512yes—
330C2×C73#242912yes—
331C2×C73#251912yes—
332C2×C73#254011yescharacteristic
333C2×C73#254211yescharacteristic
334C2×C73#255612yes—
335C2×C73#266411yescharacteristic
336C2×C73#285611yescharacteristic
337C2×#399C2×C7311yescharacteristic
338C2×#398C2×C7312yescomplemented
339C2×#396C2×C7312yes—
340C2×#389C2×C7311yescharacteristic, complemented
341C2×#388C2×C7311yescharacteristic
342C2×C4×C4⋊C4C2×C7311yescharacteristic, complemented
343#1445C2×C7311yescharacteristic, complemented
344#1444C2×C7311yescharacteristic, complemented
345#1439C2×C7311yescharacteristic
346#1437C2×C7312yes—
347C4⋊#95C2×C7312yescomplemented
348C73#1487011yescharacteristic, direct product factor, Sylow
349C22×C4⋊C4C22×C7312yes—
350C22×C4⋊C4C22×C7311yescharacteristic
351C22×C4⋊C4C22×C7312yes—
352C22×C4⋊C4C22×C7311yescharacteristic
353C22×C4⋊C4C22×C7311yescharacteristic
354C22×C4⋊C4C22×C7312yes—
355C22×C4⋊C4C22×C7312yes—
356C22×C22⋊C4C22×C7311yescharacteristic
357C22×C22⋊C4C22×C7312yes—
358C22×C22⋊C4C22×C7311yescharacteristic
359C22×C22⋊C4C22×C7312yes—
360C22×C22⋊C4C22×C7311yescharacteristic
361C22×C42C22×C7312yes—
362C22×C42C22×C7311yescharacteristic
363#399—24no—
364#398—28no—
365#396—28no—
366#389—24no—
367#388—24no—
368C4×C4⋊C4—24no—
369C2×#95C22×C7312yes—
370C2×#95C22×C7312yes—
371C2×#95C22×C7312yes—
372C2×#95C22×C7312yes—
373C2×#95C22×C7311yescharacteristic
374C2×#95C22×C7312yes—
375C2×#95C22×C7311yescharacteristic
376C2×#95C22×C7311yescharacteristic
377C2×#95C22×C7311yescharacteristic
378C25C23×C7311yescharacteristic
379C23×C4C23×C7312yes—
380C23×C4C23×C7311yescharacteristic
381C23×C4C23×C7311yescharacteristic
382C23×C4C23×C7312yes—
383C23×C4C23×C7311yescharacteristic
384C23×C4C23×C7312yes—
385C23×C4C23×C7311yescharacteristic
386C23×C4C23×C7312yes—
387C23×C4C23×C7311yescharacteristic
388C23×C4C23×C7311yescharacteristic
389C2×C4⋊C4—24no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—42no—
407C2×C4⋊C4D4×C7318yes—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—42no—
421C2×C22⋊C4Q8×C7314yes—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—24no—
425C2×C42—24no—
426C2×C42—42no—
427C2×C42D4×C7314yes—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95D4×C7314yes—
437C24—21no—
438C24—21no—
439C24—22no—
440C24—21no—
441C24—22no—
442C24—22no—
443C24—21no—
444C24—21no—
445C24—22no—
446C24—21no—
447C24C2×Q8×C7312yes—
448C24C24×C7311yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4C2×D4×C7314yes—
496C22×C4C2×D4×C7312yes—
497C22×C4C2×D4×C7312yes—
498C22×C4C2×D4×C7314yes—
499C22×C4C2×D4×C7314yes—
500C22×C4C2×D4×C7312yes—
501C22×C4C2×D4×C7312yes—
502C22×C4C2×D4×C7314yes—
503C22×C4C2×Q8×C7312yes—
504C22×C4C2×Q8×C7312yes—
505C22×C4#41×C7314yes—
506C22×C4#41×C7312yes—
507C22×C4#41×C7314yes—
508C22×C4#41×C7312yes—
509C4⋊C4—28no—
510C4⋊C4—216no—
511C4⋊C4—48no—
512C4⋊C4—44no—
513C4⋊C4—48no—
514C4⋊C4—44no—
515C4⋊C4—48no—
516C22⋊C4—28no—
517C22⋊C4—48no—
518C22⋊C4—44no—
519C22⋊C4—48no—
520C22⋊C4—44no—
521C42—28no—
522C42—48no—
523C23—22no—
524C23—24no—
525C23—24no—
526C23—22no—
527C23—22no—
528C23—41no—
529C23—42no—
530C23—41no—
531C23—42no—
532C23—41no—
533C23—42no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—41no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23C22×D4×C7311yescharacteristic
547C23C22×D4×C7311yescharacteristic
548C23C22×D4×C7312yes—
549C23C22×Q8×C7311yescharacteristic
550C23C2×#41×C7312yes—
551C23C2×#41×C7311yescharacteristic
552C23C2×#41×C7311yescharacteristic
553C23C2×#41×C7312yes—
554C23H(5,𝔽2)×C7311yescharacteristic
555C232−1+4×C7312yes—
556C232−1+4×C7311yescharacteristic
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4#121×C7314yes—
614C2×C4#121×C7318yes—
615C2×C4C22⋊Q8×C7314yes—
616C2×C4#127×C7314yes—
617C22—42no—
618C22—44no—
619C22—42no—
620C22—42no—
621C22—44no—
622C22—82no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—82no—
628C22C2×#121×C7311yescharacteristic
629C22C2×#121×C7312yes—
630C22C2×C22⋊Q8×C7311yescharacteristic
631C22#525×C7311yescharacteristic
632C22#529×C7312yes—
633C22C2×#127×C7311yescharacteristic
634C22#532×C7312yes—
635C22#532×C7311yescharacteristic
636C22#533×C7312yes—
637C22#536×C7311yescharacteristic
638C22#537×C7311yescharacteristic
639C22#539×C7312yes—
640C22#541×C7312yes—
641C22#546×C7312yes—
642C22#546×C7311yescharacteristic
643C22#547×C7312yes—
644C22#547×C7312yes—
645C22#548×C7312yes—
646C22D4×Q8×C7312yes—
647C22D4×Q8×C7311yescharacteristic
648C22#552×C7311yescharacteristic
649C22#552×C7312yes—
650C22#554×C7311yescharacteristic
651C4—24no—
652C4—24no—
653C4—24no—
654C4—28no—
655C4—44no—
656C4—42no—
657C4—44no—
658C4—81no—
659C4—81no—
660C4—82no—
661C2—82no—
662C2C73×#239611yescharacteristic
663C2C73×#241311yescharacteristic
664C2C73×#241711yescharacteristic
665C2C73×#242512yes—
666C2C73×#242912yes—
667C2C73×#251912yes—
668C2C73×#254011yescharacteristic
669C2C73×#254211yescharacteristic
670C2C73×#255612yes—
671C2C73×#266411yescharacteristic
672C2C73×#285611yescharacteristic
subgroupG/H
center, socleC24×C73C24
commutator, Frattini, cosocleC24C24×C73
prime radicalC25×C73C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#398×C73C2semidirect
4. C2×#389×C73C2semidirect
6. C2×C4×C4⋊C4×C73C2semidirect
7. C73×#1445C2semidirect
8. C73×#1444C2semidirect
11. C73×C4⋊#95C2semidirect
324. #14870C73direct (N × H)
338. C2×#398C2×C73semidirect
340. C2×#389C2×C73semidirect
342. C2×C4×C4⋊C4C2×C73semidirect
343. #1445C2×C73semidirect
344. #1444C2×C73semidirect
347. C4⋊#95C2×C73semidirect
348. C73#14870direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#399×C732
C2×#398×C732
C2×#396×C732
C2×#389×C732
C2×#388×C732
C2×C4×C4⋊C4×C732
C73×#14452
C73×#14442
C73×#14392
C73×#14372
C73×C4⋊#952
#1487073