Subgroups — C₄×#731 #66340

Order 324.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#731	C₂	1	1	yes	maximal, characteristic
2	C₄×3₋¹⁺²	C₃	1	2	yes	maximal, complemented
3	C₄×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
4	C₃×C₄×C₉	C₃	1	1	yes	maximal, characteristic, complemented
5	#731	C₄	1	1	yes	characteristic, direct product factor, Sylow
6	C₂×3₋¹⁺²	C₂×C₃	1	2	yes	—
7	C₂×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
8	C₂×C₃×C₉	C₂×C₃	1	1	yes	characteristic
9	C₃²×C₄	—	3	1	no	—
10	C₃²×C₄	C₃²	1	1	yes	characteristic
11	C₄×C₉	—	3	1	no	—
12	C₄×C₉	—	3	2	no	—
13	3₋¹⁺²	C₃×C₄	1	2	yes	complemented
14	H(3,𝔽₃)	C₃×C₄	1	1	yes	characteristic
15	C₃×C₉	C₃×C₄	1	1	yes	characteristic, complemented
16	C₂×C₃²	—	3	1	no	—
17	C₂×C₃²	C₂×C₃²	1	1	yes	characteristic
18	C₂×C₉	—	3	1	no	—
19	C₂×C₉	—	3	2	no	—
20	C₃×C₄	—	3	1	no	—
21	C₃×C₄	—	9	1	no	—
22	C₃×C₄	H(3,𝔽₃)	1	1	yes	characteristic
23	C₃²	—	3	1	no	—
24	C₃²	C₃²×C₄	1	1	yes	characteristic
25	C₉	—	3	1	no	—
26	C₉	—	3	2	no	—
27	C₂×C₃	—	3	1	no	—
28	C₂×C₃	—	9	1	no	—
29	C₂×C₃	C₂×H(3,𝔽₃)	1	1	yes	characteristic
30	C₄	#731	1	1	yes	characteristic, direct product factor, Sylow
31	C₃	—	3	1	no	—
32	C₃	—	9	1	no	—
33	C₃	C₄×H(3,𝔽₃)	1	1	yes	characteristic
34	C₂	C₂×#731	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.