Subgroups — #17989671

Order 4672.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10596842	C₂	1	2	yes	maximal
2	C₈×#64408	C₂	1	1	yes	maximal, characteristic
3	C₂×#10596842	C₄	1	4	yes	—
4	#11924036	C₄	1	1	yes	characteristic
5	C₄×#64408	C₂²	1	1	yes	characteristic
6	C₈×D₇₃	C₄	1	1	yes	characteristic
7	C₂×#64408	C₂×C₄	1	2	yes	—
8	#10596842	—	2	4	no	—
9	C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
10	#10596833	C₈	1	2	yes	complemented
11	C₈×C₇₃	C₈	1	1	yes	characteristic, complemented
12	#10596831	C₈	1	1	yes	characteristic, complemented
13	C₂×D₇₃	C₄²	1	1	yes	characteristic
14	#64408	M₁₆	1	4	yes	—
15	C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
16	Dic₇₃	C₂×C₈	1	1	yes	characteristic
17	C₂×C₇₃	C₄×C₈	1	1	yes	characteristic
18	D₇₃	#97	1	2	yes	—
19	C₇₃	#322	1	1	yes	characteristic, complemented, Sylow
20	#322	—	73	1	no	maximal, Sylow
21	C₄×C₈	—	73	2	no	—
22	C₄×C₈	—	73	1	no	—
23	C₂×C₈	—	73	1	no	—
24	C₂×C₈	—	73	1	no	—
25	C₂×C₈	—	73	4	no	—
26	C₄²	—	73	1	no	—
27	C₂×C₄	—	73	2	no	—
28	C₂×C₄	—	73	1	no	—
29	C₈	—	73	2	no	—
30	C₈	—	73	1	no	—
31	C₈	—	146	4	no	—
32	C₈	#10596842	1	1	yes	characteristic, complemented
33	C₂²	—	73	1	no	—
34	C₄	—	73	4	no	—
35	C₄	—	73	1	no	—
36	C₄	C₂×#10596842	1	1	yes	characteristic
37	C₂	—	73	2	no	—
38	C₂	C₄×#10596842	1	1	yes	characteristic

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

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