Subgroups — #4544

Order 192.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#127	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₃⋊C₈)	C₂	1	2	yes	maximal, complemented
3	#331	—	3	1	no	maximal, Sylow
4	C₂×C₃×D₄	—	2	2	no	—
5	C₂×C₃×D₄	C₄	1	2	yes	—
6	C₃×C₄²	C₂²	1	1	yes	characteristic
7	C₂×C₃⋊C₈	—	2	2	no	—
8	#127	D₃	1	1	yes	characteristic
9	C₄⋊C₈	—	3	2	no	—
10	C₂³×C₃	—	2	2	no	—
11	C₃×D₄	—	4	2	no	—
12	C₃×D₄	—	4	2	no	—
13	C₃×D₄	—	4	2	no	—
14	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
15	C₂×C₃×C₄	D₄	1	2	yes	—
16	C₃⋊C₈	—	4	2	no	—
17	C₂×D₄	—	2	2	no	—
18	C₂×D₄	Dic₃	1	2	yes	—
19	C₂×C₈	—	6	2	no	—
20	C₄²	C₂×D₃	1	1	yes	characteristic
21	C₂²×C₃	—	4	2	no	—
22	C₂²×C₃	—	4	4	no	—
23	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₃×C₄	—	2	1	no	—
25	C₃×C₄	D₈	1	2	yes	—
26	C₃×C₄	SD₁₆	1	2	yes	—
27	C₂³	—	2	2	no	—
28	D₄	—	4	2	no	—
29	D₄	—	4	2	no	—
30	D₄	—	4	2	no	—
31	C₂×C₄	C₂×Dic₃	1	1	yes	characteristic
32	C₂×C₄	#67	1	2	yes	—
33	C₈	—	12	2	no	—
34	C₂×C₃	—	8	2	no	—
35	C₂×C₃	#100	1	1	yes	characteristic
36	C₂×C₃	#102	1	2	yes	—
37	C₂²	—	4	4	no	—
38	C₂²	—	4	2	no	—
39	C₂²	#217	1	1	yes	characteristic
40	C₄	—	2	1	no	—
41	C₄	#213	1	2	yes	—
42	C₄	#214	1	2	yes	—
43	C₃	#331	1	1	yes	characteristic, complemented, Sylow
44	C₂	—	8	2	no	—
45	C₂	#832	1	2	yes	—
46	C₂	#833	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₄⋊(C₃⋊C₈)	C₂	semidirect
43. C₃	#331	semidirect

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