Subgroups — C₂×C₃×#3624 #11717841

Order 816.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₁₇	C₂	1	1	yes	maximal, characteristic
2	C₃×#3624	C₂	1	2	yes	maximal, direct product factor
3	C₂×#3624	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₃×C₁₇	C₄	1	1	yes	characteristic
5	C₃×Dic₁₇	C₄	1	1	yes	characteristic
6	C₃×Dic₁₇	C₂²	1	1	yes	characteristic
7	C₂×Dic₁₇	C₂×C₃	1	1	yes	characteristic
8	#3624	C₂×C₃	1	2	yes	direct product factor
9	C₂×C₃×C₁₇	C₈	1	2	yes	complemented
10	C₂×C₃×C₁₇	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₁₇	C₃×C₄	1	1	yes	characteristic
12	Dic₁₇	C₃×C₄	1	1	yes	characteristic
13	Dic₁₇	C₂²×C₃	1	1	yes	characteristic
14	C₃×C₁₇	C₂×C₈	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₈	—	17	1	no	maximal, Hall
16	C₂×C₁₇	C₃×C₈	1	2	yes	complemented
17	C₂×C₁₇	C₂×C₃×C₄	1	1	yes	characteristic
18	C₂×C₃×C₄	—	17	1	no	—
19	C₃×C₈	—	17	2	no	—
20	C₁₇	C₂×C₃×C₈	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₈	—	17	1	no	Sylow
22	C₂²×C₃	#595	1	1	yes	characteristic
23	C₃×C₄	—	17	1	no	—
24	C₃×C₄	—	17	1	no	—
25	C₂×C₄	—	17	1	no	—
26	C₈	—	17	2	no	—
27	C₂×C₃	#3624	1	2	yes	direct product factor
28	C₂×C₃	C₂×#595	1	1	yes	characteristic
29	C₂²	C₃×#595	1	1	yes	characteristic
30	C₄	—	17	1	no	—
31	C₄	—	17	1	no	—
32	C₃	C₂×#3624	1	1	yes	characteristic, direct product factor, Sylow
33	C₂	C₃×#3624	1	2	yes	direct product factor
34	C₂	C₂×C₃×#595	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.