Subgroups — #4494

Order 192.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#108	C₂	1	1	yes	maximal, characteristic
2	#817	C₂	1	1	yes	maximal, characteristic
3	#812	C₂	1	1	yes	maximal, characteristic
4	#365	—	3	1	no	maximal, Sylow
5	C₃×M₁₆	—	2	1	no	—
6	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₃	—	2	1	no	—
8	C₃⋊C₁₆	C₄	1	2	yes	complemented
9	M₃₂	—	3	1	no	—
10	#108	D₃	1	1	yes	characteristic
11	#106	—	3	1	no	—
12	C₂×C₃×C₄	D₄	1	1	yes	characteristic
13	C₂×Dic₃	—	4	1	no	—
14	C₃×C₈	—	4	1	no	—
15	C₃×C₈	C₂×C₄	1	1	yes	characteristic
16	C₃×C₈	Q₈	1	1	yes	characteristic
17	M₁₆	—	2	1	no	—
18	C₂×C₈	C₂×D₃	1	1	yes	characteristic
19	C₄⋊C₄	—	6	1	no	—
20	C₁₆	—	3	2	no	—
21	C₂²×C₃	SD₁₆	1	1	yes	characteristic
22	C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
23	C₃×C₄	SD₁₆	1	1	yes	characteristic
24	Dic₃	—	8	1	no	—
25	C₂×C₄	—	12	1	no	—
26	C₂×C₄	#67	1	1	yes	characteristic
27	C₈	—	4	1	no	—
28	C₈	Dic₆	1	1	yes	characteristic
29	C₈	C₄×D₃	1	1	yes	characteristic
30	C₂×C₃	—	2	1	no	—
31	C₂×C₃	#106	1	1	yes	characteristic
32	C₂²	#215	1	1	yes	characteristic
33	C₄	—	24	1	no	—
34	C₄	Dic₃⋊C₄	1	1	yes	characteristic
35	C₄	#214	1	1	yes	characteristic
36	C₃	#365	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	2	1	no	—
38	C₂	#808	1	1	yes	characteristic

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

N	H ≅ G/N	type
8. C₃⋊C₁₆	C₄	semidirect
36. C₃	#365	semidirect

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