Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
240 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 68 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×#4904 | C2 | semidirect |
| 2. C2×C3×D48 | C2 | semidirect |
| 3. #10589365 | C2 | semidirect |
| 4. #10589072 | C2 | semidirect |
| 5. #10589070 | C2 | semidirect |
| 11. C3×Dic24 | C22 | semidirect |
| 15. C3×D48 | C22 | semidirect |
| 16. C3⋊(C3⋊C32) | C22 | semidirect |
| 19. #4904 | D3 | semidirect |
| 20. C2×D48 | D3 | semidirect |
| 51. Dic24 | C2×D3 | semidirect |
| 55. D48 | C2×D3 | semidirect |
| 167. C32 | #2263 | semidirect |
| 196. C3 | #71458 | semidirect |
| 197. C3 | #71509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4904 | 2 |
| C2×C3×D48 | 2 |
| #10589365 | 2 |
| #10589072 | 2 |
| #10589070 | 2 |
| #71509 | 3 |
| #71458 | 3 |