Subgroups — #17989686

Order 4672.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14556687	C₂	1	2	yes	maximal, complemented
2	C₂×#11924038	C₂	1	1	yes	maximal, characteristic
3	#11924040	—	2	2	no	—
4	#11924038	—	2	2	no	—
5	C₂×#10596833	C₄	1	1	yes	characteristic
6	C₂×#10596833	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₇₃	C₄	1	1	yes	characteristic
8	C₂²×D₇₃	C₈	1	1	yes	characteristic
9	C₂×C₄×C₇₃	C₈	1	1	yes	characteristic
10	C₂×Dic₇₃	C₂×C₄	1	1	yes	characteristic
11	C₄×D₇₃	—	2	1	no	—
12	C₄×D₇₃	—	2	1	no	—
13	#10596833	—	2	1	no	—
14	#10596833	D₄	1	2	yes	—
15	C₂²×C₇₃	C₂×C₈	1	1	yes	characteristic
16	C₂×D₇₃	—	2	1	no	—
17	C₂×D₇₃	—	4	1	no	—
18	C₄×C₇₃	—	2	1	no	—
19	Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
20	Dic₇₃	M₁₆	1	1	yes	characteristic
21	C₂×C₇₃	—	2	1	no	—
22	C₂×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
23	D₇₃	—	4	1	no	—
24	C₇₃	#349	1	1	yes	characteristic, complemented, Sylow
25	#349	—	73	1	no	maximal, Sylow
26	C₂×M₁₆	—	73	1	no	—
27	M₃₂	—	73	2	no	—
28	C₂²×C₄	—	73	1	no	—
29	M₁₆	—	146	2	no	—
30	C₂×C₈	—	73	1	no	—
31	C₂×C₈	—	73	1	no	—
32	C₁₆	—	146	2	no	—
33	C₂³	—	73	1	no	—
34	C₂×C₄	—	73	1	no	—
35	C₂×C₄	—	146	1	no	—
36	C₂×C₄	—	146	1	no	—
37	C₂×C₄	#10596842	1	1	yes	characteristic
38	C₈	—	73	2	no	—
39	C₈	—	146	1	no	—
40	C₂²	—	292	1	no	—
41	C₂²	—	146	1	no	—
42	C₂²	C₂×#10596842	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	73	1	no	—
45	C₄	—	73	1	no	—
46	C₂	—	2	1	no	—
47	C₂	—	292	1	no	—
48	C₂	C₂²⋊#10596842	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #14556687	C₂	semidirect
24. C₇₃	#349	semidirect

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