Subgroups — #17989709

Order 4672.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14556688	C₂	1	3	yes	maximal, complemented
2	#14556686	C₂	1	3	yes	maximal, complemented
3	#14556679	C₂	1	1	yes	maximal, characteristic
4	#11924040	C₂²	1	1	yes	characteristic
5	#11924040	C₂²	1	3	yes	—
6	#11924038	C₄	1	3	yes	—
7	#11924036	C₂²	1	3	yes	—
8	#11924029	C₄	1	1	yes	characteristic
9	Q₈×C₇₃	C₈	1	1	yes	characteristic
10	D₂₉₂	C₈	1	3	yes	—
11	C₄×D₇₃	C₂×C₄	1	3	yes	—
12	#10596833	C₂×C₄	1	3	yes	—
13	#10596833	C₂³	1	1	yes	characteristic
14	C₂×D₇₃	C₂×C₈	1	3	yes	—
15	C₄×C₇₃	C₂×C₈	1	3	yes	—
16	Dic₇₃	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₇₃	C₂²×C₈	1	1	yes	characteristic
18	D₇₃	—	2	3	no	—
19	C₇₃	#504	1	1	yes	characteristic, complemented, Sylow
20	#504	—	73	1	no	maximal, Sylow
21	#131	—	73	1	no	—
22	M₃₂	—	73	3	no	—
23	C₂×C₁₆	—	73	3	no	—
24	#41	—	73	1	no	—
25	M₁₆	—	73	3	no	—
26	C₂×C₈	—	73	3	no	—
27	C₁₆	—	73	1	no	—
28	C₁₆	—	73	3	no	—
29	Q₈	#10596842	1	1	yes	characteristic
30	D₄	—	73	3	no	—
31	C₂×C₄	—	73	3	no	—
32	C₈	—	73	1	no	—
33	C₈	—	73	3	no	—
34	C₂²	—	73	3	no	—
35	C₄	—	73	1	no	—
36	C₄	C₂×#10596842	1	3	yes	—
37	C₂	—	146	3	no	—
38	C₂	C₂²×#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.