Subgroups — C₂×#14556681 #17989693

Order 4672.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14556681	C₂	1	2	yes	maximal, direct product factor
2	C₂×#11924031	C₂	1	1	yes	maximal, characteristic
3	#11924031	C₄	1	1	yes	characteristic
4	#11924031	C₂²	1	1	yes	characteristic
5	C₂×#10596831	C₄	1	1	yes	characteristic
6	C₂×C₄×C₇₃	C₈	1	1	yes	characteristic
7	#10596831	C₈	1	1	yes	characteristic
8	#10596831	C₂×C₄	1	1	yes	characteristic
9	C₂²×C₇₃	C₁₆	1	1	yes	characteristic
10	C₄×C₇₃	C₁₆	1	1	yes	characteristic
11	C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
12	C₂×C₇₃	C₃₂	1	2	yes	complemented
13	C₂×C₇₃	C₂×C₁₆	1	1	yes	characteristic
14	C₇₃	C₂×C₃₂	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₃₂	—	73	1	no	maximal, Sylow
16	C₂×C₁₆	—	73	1	no	—
17	C₃₂	—	73	2	no	—
18	C₂×C₈	—	73	1	no	—
19	C₁₆	—	73	1	no	—
20	C₁₆	—	73	1	no	—
21	C₂×C₄	#10596842	1	1	yes	characteristic
22	C₈	—	73	1	no	—
23	C₈	—	73	1	no	—
24	C₂²	#11924040	1	1	yes	characteristic
25	C₄	#11924040	1	1	yes	characteristic
26	C₄	C₂×#10596842	1	1	yes	characteristic
27	C₂	#14556681	1	2	yes	direct product factor
28	C₂	C₂×#11924040	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.