Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
941 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 941 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#5510 | C2 | semidirect |
| 2. C2×#63825 | C2 | semidirect |
| 3. #10592687 | C2 | semidirect |
| 4. C2×#63568 | C2 | semidirect |
| 5. C3×#4530 | C2 | semidirect |
| 25. #5510 | D3 | semidirect |
| 32. #4530 | D3 | semidirect |
| 40. C2×C4⋊(C3⋊D3) | D4 | semidirect |
| 56. C3×#208 | D4 | semidirect |
| 188. #208 | D12 | semidirect |
| 383. C32 | #2006 | semidirect |
| 452. C3 | #69008 | semidirect |
| 453. C3 | #71879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5510 | 2 |
| C2×#63825 | 2 |
| #10592687 | 2 |
| C2×#63568 | 2 |
| C3×#4530 | 2 |
| #71879 | 3 |
| #69008 | 3 |