Subgroups — #17989682

Order 4672.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14556686	C₂	1	2	yes	maximal
2	C₈×#64408	C₂	1	1	yes	maximal, characteristic
3	#11924040	C₄	1	4	yes	complemented
4	#11924036	C₂²	1	1	yes	characteristic
5	C₄×#64408	C₄	1	1	yes	characteristic
6	C₈×D₇₃	C₄	1	1	yes	characteristic
7	C₂×#64408	C₈	1	2	yes	—
8	C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
9	#10596833	C₂×C₄	1	2	yes	—
10	C₈×C₇₃	C₈	1	1	yes	characteristic
11	#10596831	C₈	1	1	yes	characteristic
12	C₂×D₇₃	C₂×C₈	1	1	yes	characteristic
13	#64408	—	2	2	no	—
14	C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
15	Dic₇₃	C₄²	1	1	yes	characteristic
16	C₂×C₇₃	C₄×C₈	1	1	yes	characteristic
17	D₇₃	M₃₂	1	2	yes	—
18	C₇₃	#346	1	1	yes	characteristic, complemented, Sylow
19	#346	—	73	1	no	maximal, Sylow
20	C₂×C₁₆	—	73	2	no	—
21	C₄×C₈	—	73	1	no	—
22	C₂×C₈	—	73	1	no	—
23	C₂×C₈	—	73	1	no	—
24	C₄²	—	73	1	no	—
25	C₁₆	—	73	4	no	—
26	C₂×C₄	—	73	1	no	—
27	C₂×C₄	—	73	2	no	—
28	C₈	—	73	2	no	—
29	C₈	—	73	1	no	—
30	C₈	#10596842	1	1	yes	characteristic
31	C₂²	—	73	1	no	—
32	C₄	—	73	1	no	—
33	C₄	—	146	2	no	—
34	C₄	C₂×#10596842	1	1	yes	characteristic
35	C₂	—	73	2	no	—
36	C₂	C₄×#10596842	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #11924040	C₄	semidirect
18. C₇₃	#346	semidirect

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