Subgroups — #3674

Order 144.

27 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₉	C₂	1	1	yes	maximal, characteristic
2	Dic₁₈	C₂	1	1	yes	maximal, characteristic
3	C₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#216	—	3	1	no	maximal
5	C₄×C₉	—	2	1	no	—
6	C₄×C₉	C₂²	1	1	yes	characteristic
7	Dic₉	—	2	1	no	—
8	C₃×Q₈	D₃	1	1	yes	characteristic
9	Dic₆	—	3	1	no	—
10	C₃⋊C₈	—	3	1	no	—
11	C₂×C₉	D₄	1	1	yes	characteristic
12	Q₁₆	—	9	1	no	Sylow
13	C₃×C₄	—	2	1	no	—
14	C₃×C₄	C₂×D₃	1	1	yes	characteristic
15	Dic₃	—	6	1	no	—
16	C₉	Q₁₆	1	1	yes	characteristic, complemented, Sylow
17	Q₈	—	9	1	no	—
18	Q₈	D₉	1	1	yes	characteristic
19	C₈	—	9	1	no	—
20	C₂×C₃	#67	1	1	yes	characteristic
21	C₄	—	2	1	no	—
22	C₄	—	18	1	no	—
23	C₄	C₂×D₉	1	1	yes	characteristic
24	C₃	#216	1	1	yes	characteristic
25	C₂	#611	1	1	yes	characteristic

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

N	H ≅ G/N	type
16. C₉	Q₁₆	semidirect

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