Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
849 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 849 conjugacy classes of subgroups — too many to draw. Only its 164 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. C2×#63802 | C2 | semidirect |
| 3. C2×C16×C3⋊D3 | C2 | semidirect |
| 4. C2×C3×#800 | C2 | semidirect |
| 5. C2×#63547 | C2 | semidirect |
| 6. #10590235 | C2 | direct (N × H) |
| 11. C2×C3×Dic12 | C22 | semidirect |
| 16. #63802 | C22 | semidirect |
| 19. C2×C32×C16 | C22 | semidirect |
| 20. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 21. C16×C3⋊D3 | C22 | semidirect |
| 22. C3×#800 | C22 | semidirect |
| 23. #63547 | C22 | semidirect |
| 30. C2×#800 | D3 | semidirect |
| 49. C3×Dic12 | C23 | semidirect |
| 54. C32×C16 | C23 | semidirect |
| 55. C3⋊(C3⋊C16) | C23 | semidirect |
| 67. C2×Dic12 | C2×D3 | semidirect |
| 73. C2×C3×C16 | C2×D3 | semidirect |
| 78. #800 | C2×D3 | semidirect |
| 131. Dic12 | C22×D3 | semidirect |
| 139. C3×C16 | C22×D3 | semidirect |
| 143. C2×C3⋊D3 | SD32 | semidirect |
| 167. C2×C16 | D32 | semidirect |
| 201. C2×C32 | C2×SD32 | semidirect |
| 203. C3⋊D3 | C2×SD32 | semidirect |
| 227. C16 | C2×D32 | semidirect |
| 247. C32 | C22×SD32 | semidirect |
| 270. C2×C3 | D3×SD32 | semidirect |
| 286. C3 | C2×D3×SD32 | semidirect |
| 289. C2 | #10590235 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63802 | 2 |
| C2×#63797 | 2 |
| C2×C16×C3⋊D3 | 2 |
| C2×C3×#800 | 2 |
| C2×#63547 | 2 |
| #10590235 | 2 |
| C2×D3×SD32 | 3 |