Finite Group Databasebeta

← C73×#18804 #32928208

Subgroups — C73×#18804 #32928208

Order 18688.

968 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3475C211yesmaximal, characteristic
2C73×#3229C211yesmaximal, characteristic, complemented
3C2×#474×C73C211yesmaximal, characteristic, complemented
4C73×#3039C211yesmaximal, characteristic, complemented
5C73×#1654C212yesmaximal, complemented
6C73×#1652C212yesmaximal, complemented
7C73×#1646C212yesmaximal, complemented
8C73×#1644C212yesmaximal, complemented
9C73×#1550C211yesmaximal, characteristic, complemented
10C73×#1486C211yesmaximal, characteristic, complemented
11C73×#1477C211yesmaximal, characteristic, complemented
12C2×#137×C73—21no—
13#556×C73C2211yescharacteristic
14#555×C73C2211yescharacteristic
15#554×C73C2211yescharacteristic
16#553×C73—21no—
17#552×C73—21no—
18#552×C73—21no—
19#551×C73—22no—
20#547×C73C2211yescharacteristic
21#546×C73—21no—
22#533×C73C2211yescharacteristic
23C2×C4⋊Q8×C73C2211yescharacteristic
24#529×C73—22no—
25#529×C73—21no—
26#525×C73—21no—
27C4×#41×C73—21no—
28C4×#41×C73C2211yescharacteristic
29C2×C4×D4×C73C2211yescharacteristic
30C2×#117×C73—21no—
31#498×C73C2212yescomplemented
32#487×C73C2212yescomplemented
33#483×C73—22no—
34#475×C73—22no—
35#474×C73—21no—
36#474×C73—21no—
37#474×C73C2212yes—
38#474×C73C2212yes—
39#462×C73—21no—
40#462×C73C2212yescomplemented
41#461×C73—21no—
42#461×C73C2212yescomplemented
43#431×C73C2211yescharacteristic
44C2×#107×C73—21no—
45#423×C73C2211yescharacteristic
46C2×C4⋊C8×C73C2211yescharacteristic
47#419×C73—21no—
48C2×#102×C73—21no—
49#333×C73C2212yescomplemented
50#332×C73C2212yescomplemented
51Q8⋊C8×C73C2212yescomplemented
52D4⋊C8×C73C2212yes—
53D4⋊C8×C73C2212yes—
54D4⋊C8×C73C2212yescomplemented
55C2×#41×C73—21no—
56C2×#41×C73D411yescharacteristic
57C22×Q8×C73—21no—
58C22×D4×C73D411yescharacteristic
59C23×C4×C73—21no—
60#137×C73—44no—
61C2×Q16×C73—22no—
62C2×SD16×C73—22no—
63C2×M16×C73—21no—
64C22×C8×C73—21no—
65C4⋊Q8×C73—21no—
66C4⋊Q8×C73—21no—
67C4⋊Q8×C73—21no—
68C4⋊Q8×C73C2312yes—
69C4⋊Q8×C73C2311yescharacteristic
70C4⋊Q8×C73C2311yescharacteristic
71#126×C73—22no—
72#126×C73—22no—
73#126×C73—22no—
74#125×C73—22no—
75#125×C73—21no—
76#125×C73—21no—
77#124×C73—22no—
78#124×C73—21no—
79#123×C73—22no—
80#123×C73—22no—
81#123×C73—22no—
82#123×C73—22no—
83C22⋊Q8×C73—21no—
84C22⋊Q8×C73—21no—
85C22⋊Q8×C73—22no—
86C22⋊Q8×C73—21no—
87C22⋊Q8×C73—21no—
88C22⋊Q8×C73D412yes—
89#121×C73—22no—
90#121×C73—21no—
91#121×C73—21no—
92#121×C73—21no—
93#120×C73—22no—
94C4×Q8×C73—21no—
95C4×Q8×C73—21no—
96C4×Q8×C73D411yescharacteristic
97C4×Q8×C73D412yes—
98C4×Q8×C73C2311yescharacteristic
99C4×D4×C73—22no—
100C4×D4×C73—22no—
101C4×D4×C73—22no—
102C4×D4×C73—21no—
103C4×D4×C73—21no—
104C4×D4×C73—21no—
105C4×D4×C73—21no—
106C4×D4×C73—21no—
107C4×D4×C73D411yescharacteristic
108C4×D4×C73D411yescharacteristic
109C4×D4×C73D411yescharacteristic
110C4×D4×C73C2311yescharacteristic
111C4×D4×C73C2311yescharacteristic
112C4×D4×C73C2311yescharacteristic
113#117×C73—22no—
114#117×C73—22no—
115#117×C73—22no—
116#117×C73—21no—
117#117×C73—21no—
118#117×C73—21no—
119#117×C73—21no—
120#117×C73—21no—
121#117×C73D411yescharacteristic
122C2×C4⋊C4×C73—21no—
123C2×C4⋊C4×C73—21no—
124C2×C4⋊C4×C73—21no—
125C2×C4⋊C4×C73—21no—
126C2×C4⋊C4×C73D411yescharacteristic
127C2×C22⋊C4×C73—22no—
128C2×C22⋊C4×C73—21no—
129C2×C42×C73—22no—
130C2×C42×C73—21no—
131C2×C42×C73C2311yescharacteristic
132#107×C73—22no—
133#107×C73—22no—
134#106×C73—24no—
135C4⋊C8×C73—21no—
136C4⋊C8×C73—21no—
137C4⋊C8×C73—21no—
138C4⋊C8×C73C2312yes—
139C4⋊C8×C73C2312yes—
140#103×C73—24no—
141#103×C73—22no—
142#103×C73—22no—
143#102×C73—22no—
144#102×C73—22no—
145C22⋊C8×C73—21no—
146C4×C8×C73C2312yes—
147C24×C73—21no—
148#41×C73—22no—
149#41×C73—22no—
150#41×C73—42no—
151#41×C73—42no—
152C2×Q8×C73—21no—
153C2×Q8×C73—22no—
154C2×Q8×C73—41no—
155C2×Q8×C73—42no—
156C2×Q8×C73—42no—
157C2×Q8×C73C2×D411yescharacteristic
158C2×Q8×C73C2×D412yes—
159C2×D4×C73—22no—
160C2×D4×C73—22no—
161C2×D4×C73—21no—
162C2×D4×C73—22no—
163C2×D4×C73—21no—
164C2×D4×C73—41no—
165C2×D4×C73C2×D411yescharacteristic
166C2×D4×C73C2×D411yescharacteristic
167C2×D4×C73C2×D411yescharacteristic
168C22×C4×C73—22no—
169C22×C4×C73—21no—
170C22×C4×C73—22no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—42no—
179C22×C4×C73—42no—
180C22×C4×C73—41no—
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73C2×D411yescharacteristic
184Q16×C73—44no—
185SD16×C73—44no—
186M16×C73—42no—
187C2×C8×C73—22no—
188C2×C8×C73—22no—
189C2×C8×C73—22no—
190C2×C8×C73—42no—
191C4⋊C4×C73—22no—
192C4⋊C4×C73—22no—
193C4⋊C4×C73—22no—
194C4⋊C4×C73—22no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—22no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73—22no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—22no—
204C4⋊C4×C73—22no—
205C4⋊C4×C73—41no—
206C4⋊C4×C73—41no—
207C4⋊C4×C73C2×D411yescharacteristic
208C4⋊C4×C73C2×D411yescharacteristic
209C4⋊C4×C73C2×D412yes—
210C4⋊C4×C73C2×D411yescharacteristic
211C4⋊C4×C73C2×D411yescharacteristic
212C22⋊C4×C73—22no—
213C22⋊C4×C73—22no—
214C22⋊C4×C73—22no—
215C22⋊C4×C73—22no—
216C22⋊C4×C73—22no—
217C22⋊C4×C73—22no—
218C22⋊C4×C73—21no—
219C22⋊C4×C73—22no—
220C22⋊C4×C73—21no—
221C22⋊C4×C73—21no—
222C22⋊C4×C73—21no—
223C22⋊C4×C73—21no—
224C22⋊C4×C73—21no—
225C22⋊C4×C73—21no—
226C42×C73—22no—
227C42×C73—22no—
228C42×C73—21no—
229C42×C73—22no—
230C42×C73—21no—
231C42×C73—21no—
232C42×C73C2×D411yescharacteristic
233C42×C73C2×D411yescharacteristic
234C42×C73C2×D411yescharacteristic
235C42×C73C2411yescharacteristic
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—42no—
240C23×C73—42no—
241C23×C73—81no—
242C23×C73#12011yescharacteristic
243Q8×C73—21no—
244Q8×C73—21no—
245Q8×C73—42no—
246Q8×C73—41no—
247Q8×C73—41no—
248Q8×C73—42no—
249Q8×C73—42no—
250Q8×C73—82no—
251D4×C73—21no—
252D4×C73—21no—
253D4×C73—21no—
254D4×C73—21no—
255D4×C73—21no—
256D4×C73—42no—
257D4×C73—44no—
258D4×C73—42no—
259D4×C73—82no—
260D4×C73#13712yescomplemented
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73—21no—
270C2×C4×C73—41no—
271C2×C4×C73—44no—
272C2×C4×C73—42no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—42no—
280C2×C4×C73—42no—
281C2×C4×C73—42no—
282C2×C4×C73—42no—
283C2×C4×C73—81no—
284C2×C4×C73—82no—
285C2×C4×C73—82no—
286C2×C4×C73#12011yescharacteristic
287C2×C4×C73#12011yescharacteristic
288C2×C4×C73#12011yescharacteristic
289C2×C4×C73#13512yes—
290C2×C4×C73AGL(1,ℤ/8)12yes—
291C2×C4×C73C22×D411yescharacteristic
292C2×C4×C73C22×D411yescharacteristic
293C2×C4×C73C22×D411yescharacteristic
294C8×C73—42no—
295C8×C73—42no—
296C8×C73—42no—
297C22×C73—21no—
298C22×C73—21no—
299C22×C73—22no—
300C22×C73—41no—
301C22×C73—41no—
302C22×C73—41no—
303C22×C73—41no—
304C22×C73—41no—
305C22×C73—41no—
306C22×C73—41no—
307C22×C73—41no—
308C22×C73—84no—
309C22×C73#44912yes—
310C22×C73C2×#12011yescharacteristic
311C4×C73—21no—
312C4×C73—21no—
313C4×C73—21no—
314C4×C73—41no—
315C4×C73—41no—
316C4×C73—41no—
317C4×C73—41no—
318C4×C73—42no—
319C4×C73—41no—
320C4×C73—42no—
321C4×C73—82no—
322C4×C73#44912yes—
323C4×C73C2×#13511yescharacteristic
324C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
325C4×C73C2×#13711yescharacteristic
326C4×C73#57511yescharacteristic
327#18804C7311yesmaximal, characteristic, direct product factor, Sylow
328C2×C73—22no—
329C2×C73—42no—
330C2×C73—81no—
331C2×C73—81no—
332C2×C73C2×#44911yescharacteristic
333C2×C73#300711yescharacteristic
334C2×C73#302211yescharacteristic
335#3475C2×C7311yescharacteristic
336#3229C2×C7311yescharacteristic, complemented
337C2×#474C2×C7311yescharacteristic, complemented
338#3039C2×C7311yescharacteristic, complemented
339#1654C2×C7312yescomplemented
340#1652C2×C7312yescomplemented
341#1646C2×C7312yescomplemented
342#1644C2×C7312yescomplemented
343#1550C2×C7311yescharacteristic, complemented
344#1486C2×C7311yescharacteristic, complemented
345#1477C2×C7311yescharacteristic, complemented
346C73#1880411yescharacteristic, direct product factor, Sylow
347C2×#137—21no—
348#556C22×C7311yescharacteristic
349#555C22×C7311yescharacteristic
350#554C22×C7311yescharacteristic
351#553—21no—
352#552—21no—
353#552—21no—
354#551—22no—
355#547C22×C7311yescharacteristic
356#546—21no—
357#533C22×C7311yescharacteristic
358C2×C4⋊Q8C22×C7311yescharacteristic
359#529—22no—
360#529—21no—
361#525—21no—
362C4×#41—21no—
363C4×#41C22×C7311yescharacteristic
364C2×C4×D4C22×C7311yescharacteristic
365C2×#117—21no—
366#498C22×C7312yescomplemented
367#487C22×C7312yescomplemented
368#483—22no—
369#475—22no—
370#474—21no—
371#474—21no—
372#474C22×C7312yes—
373#474C22×C7312yes—
374#462—21no—
375#462C22×C7312yescomplemented
376#461—21no—
377#461C22×C7312yescomplemented
378#431C22×C7311yescharacteristic
379C2×#107—21no—
380#423C22×C7311yescharacteristic
381C2×C4⋊C8C22×C7311yescharacteristic
382#419—21no—
383C2×#102—21no—
384#333C22×C7312yescomplemented
385#332C22×C7312yescomplemented
386Q8⋊C8C22×C7312yescomplemented
387D4⋊C8C22×C7312yes—
388D4⋊C8C22×C7312yes—
389D4⋊C8C22×C7312yescomplemented
390C2×#41—21no—
391C2×#41D4×C7311yescharacteristic
392C22×Q8—21no—
393C22×D4D4×C7311yescharacteristic
394C23×C4—21no—
395#137—44no—
396C2×Q16—22no—
397C2×SD16—22no—
398C2×M16—21no—
399C22×C8—21no—
400C4⋊Q8—21no—
401C4⋊Q8—21no—
402C4⋊Q8—21no—
403C4⋊Q8C23×C7312yes—
404C4⋊Q8C23×C7311yescharacteristic
405C4⋊Q8C23×C7311yescharacteristic
406#126—22no—
407#126—22no—
408#126—22no—
409#125—22no—
410#125—21no—
411#125—21no—
412#124—22no—
413#124—21no—
414#123—22no—
415#123—22no—
416#123—22no—
417#123—22no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—22no—
421C22⋊Q8—21no—
422C22⋊Q8—21no—
423C22⋊Q8D4×C7312yes—
424#121—22no—
425#121—21no—
426#121—21no—
427#121—21no—
428#120—22no—
429C4×Q8—21no—
430C4×Q8—21no—
431C4×Q8D4×C7311yescharacteristic
432C4×Q8D4×C7312yes—
433C4×Q8C23×C7311yescharacteristic
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4D4×C7311yescharacteristic
443C4×D4D4×C7311yescharacteristic
444C4×D4D4×C7311yescharacteristic
445C4×D4C23×C7311yescharacteristic
446C4×D4C23×C7311yescharacteristic
447C4×D4C23×C7311yescharacteristic
448#117—22no—
449#117—22no—
450#117—22no—
451#117—21no—
452#117—21no—
453#117—21no—
454#117—21no—
455#117—21no—
456#117D4×C7311yescharacteristic
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4D4×C7311yescharacteristic
462C2×C22⋊C4—22no—
463C2×C22⋊C4—21no—
464C2×C42—22no—
465C2×C42—21no—
466C2×C42C23×C7311yescharacteristic
467#107—22no—
468#107—22no—
469#106—24no—
470C4⋊C8—21no—
471C4⋊C8—21no—
472C4⋊C8—21no—
473C4⋊C8C23×C7312yes—
474C4⋊C8C23×C7312yes—
475#103—24no—
476#103—22no—
477#103—22no—
478#102—22no—
479#102—22no—
480C22⋊C8—21no—
481C4×C8C23×C7312yes—
482C24—21no—
483#41—22no—
484#41—22no—
485#41—42no—
486#41—42no—
487C2×Q8—21no—
488C2×Q8—22no—
489C2×Q8—41no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8C2×D4×C7311yescharacteristic
493C2×Q8C2×D4×C7312yes—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—21no—
497C2×D4—22no—
498C2×D4—21no—
499C2×D4—41no—
500C2×D4C2×D4×C7311yescharacteristic
501C2×D4C2×D4×C7311yescharacteristic
502C2×D4C2×D4×C7311yescharacteristic
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—41no—
516C22×C4C2×D4×C7311yescharacteristic
517C22×C4C2×D4×C7311yescharacteristic
518C22×C4C2×D4×C7311yescharacteristic
519Q16—44no—
520SD16—44no—
521M16—42no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—42no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—21no—
531C4⋊C4—22no—
532C4⋊C4—21no—
533C4⋊C4—22no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4C2×D4×C7311yescharacteristic
543C4⋊C4C2×D4×C7311yescharacteristic
544C4⋊C4C2×D4×C7312yes—
545C4⋊C4C2×D4×C7311yescharacteristic
546C4⋊C4C2×D4×C7311yescharacteristic
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—21no—
554C22⋊C4—22no—
555C22⋊C4—21no—
556C22⋊C4—21no—
557C22⋊C4—21no—
558C22⋊C4—21no—
559C22⋊C4—21no—
560C22⋊C4—21no—
561C42—22no—
562C42—22no—
563C42—21no—
564C42—22no—
565C42—21no—
566C42—21no—
567C42C2×D4×C7311yescharacteristic
568C42C2×D4×C7311yescharacteristic
569C42C2×D4×C7311yescharacteristic
570C42C24×C7311yescharacteristic
571C23—21no—
572C23—21no—
573C23—21no—
574C23—42no—
575C23—42no—
576C23—81no—
577C23#120×C7311yescharacteristic
578Q8—21no—
579Q8—21no—
580Q8—42no—
581Q8—41no—
582Q8—41no—
583Q8—42no—
584Q8—42no—
585Q8—82no—
586D4—21no—
587D4—21no—
588D4—21no—
589D4—21no—
590D4—21no—
591D4—42no—
592D4—44no—
593D4—42no—
594D4—82no—
595D4#137×C7312yescomplemented
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—41no—
606C2×C4—44no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—42no—
618C2×C4—81no—
619C2×C4—82no—
620C2×C4—82no—
621C2×C4#120×C7311yescharacteristic
622C2×C4#120×C7311yescharacteristic
623C2×C4#120×C7311yescharacteristic
624C2×C4#135×C7312yes—
625C2×C4AGL(1,ℤ/8)×C7312yes—
626C2×C4C22×D4×C7311yescharacteristic
627C2×C4C22×D4×C7311yescharacteristic
628C2×C4C22×D4×C7311yescharacteristic
629C8—42no—
630C8—42no—
631C8—42no—
632C22—21no—
633C22—21no—
634C22—22no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—84no—
644C22#449×C7312yes—
645C22C2×#120×C7311yescharacteristic
646C4—21no—
647C4—21no—
648C4—21no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—42no—
654C4—41no—
655C4—42no—
656C4—82no—
657C4#449×C7312yes—
658C4C2×#135×C7311yescharacteristic
659C4C2×AGL(1,ℤ/8)×C7311yescharacteristic
660C4C2×#137×C7311yescharacteristic
661C4#575×C7311yescharacteristic
662C2—22no—
663C2—42no—
664C2—81no—
665C2—81no—
666C2C2×#449×C7311yescharacteristic
667C2C73×#300711yescharacteristic
668C2C73×#302211yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3475C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#3229C2semidirect
3. C2×#474×C73C2semidirect
4. C73×#3039C2semidirect
5. C73×#1654C2semidirect
6. C73×#1652C2semidirect
7. C73×#1646C2semidirect
8. C73×#1644C2semidirect
9. C73×#1550C2semidirect
10. C73×#1486C2semidirect
11. C73×#1477C2semidirect
31. #498×C73C22semidirect
32. #487×C73C22semidirect
40. #462×C73C22semidirect
42. #461×C73C22semidirect
49. #333×C73C22semidirect
50. #332×C73C22semidirect
51. Q8⋊C8×C73C22semidirect
54. D4⋊C8×C73C22semidirect
260. D4×C73#137semidirect
327. #18804C73direct (N × H)
336. #3229C2×C73semidirect
337. C2×#474C2×C73semidirect
338. #3039C2×C73semidirect
339. #1654C2×C73semidirect
340. #1652C2×C73semidirect
341. #1646C2×C73semidirect
342. #1644C2×C73semidirect
343. #1550C2×C73semidirect
344. #1486C2×C73semidirect
345. #1477C2×C73semidirect
346. C73#18804direct (N × H)
366. #498C22×C73semidirect
367. #487C22×C73semidirect
375. #462C22×C73semidirect
377. #461C22×C73semidirect
384. #333C22×C73semidirect
385. #332C22×C73semidirect
386. Q8⋊C8C22×C73semidirect
389. D4⋊C8C22×C73semidirect
595. D4#137×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#34752
C73×#32292
C2×#474×C732
C73×#30392
C73×#16542
C73×#16522
C73×#16462
C73×#16442
C73×#15502
C73×#14862
C73×#14772
#1880473