Subgroups — #17989508

Order 4672.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924031	C₂	1	2	yes	maximal
2	C₈×Dic₇₃	C₂	1	1	yes	maximal, characteristic
3	#11924031	—	2	2	no	—
4	C₂×#10596831	C₂²	1	1	yes	characteristic
5	C₄×Dic₇₃	C₄	1	1	yes	characteristic
6	C₂×C₈×C₇₃	C₄	1	1	yes	characteristic
7	C₂×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
8	C₂×Dic₇₃	C₈	1	1	yes	characteristic
9	C₂×Dic₇₃	C₈	1	1	yes	characteristic
10	C₈×C₇₃	—	2	1	no	—
11	#10596831	D₄	1	1	yes	characteristic
12	#10596831	Q₈	1	1	yes	characteristic
13	C₂²×C₇₃	C₂×C₈	1	1	yes	characteristic
14	C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₇₃	M₁₆	1	1	yes	characteristic
16	Dic₇₃	—	2	1	no	—
17	Dic₇₃	C₁₆	1	2	yes	complemented
18	C₂×C₇₃	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₇₃	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₇₃	M₃₂	1	1	yes	characteristic
21	C₇₃	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄⋊C₁₆	—	73	1	no	maximal, Sylow
23	C₂×C₁₆	—	73	2	no	—
24	C₄×C₈	—	73	1	no	—
25	C₂×C₈	—	73	1	no	—
26	C₂×C₈	#64408	1	1	yes	characteristic
27	C₄²	—	73	1	no	—
28	C₁₆	—	146	2	no	—
29	C₂×C₄	—	73	1	no	—
30	C₂×C₄	—	73	1	no	—
31	C₂×C₄	C₂×#64408	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	—	73	1	no	—
34	C₈	—	73	1	no	—
35	C₂²	#11924036	1	1	yes	characteristic
36	C₄	—	73	2	no	—
37	C₄	—	146	1	no	—
38	C₄	C₄⋊#64408	1	1	yes	characteristic
39	C₄	#11924037	1	1	yes	characteristic
40	C₂	#14556658	1	1	yes	characteristic
41	C₂	#14556664	1	1	yes	characteristic
42	C₂	#14556666	1	1	yes	characteristic

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

N	H ≅ G/N	type
17. Dic₇₃	C₁₆	semidirect
21. C₇₃	C₄⋊C₁₆	semidirect

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