Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2400 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 2400 conjugacy classes of subgroups — too many to draw. Only its 565 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 |
|---|---|---|
| 2. C32×#518 | C2 | semidirect |
| 3. #10596269 | C2 | semidirect |
| 4. #10592705 | C2 | semidirect |
| 5. C2×#63633 | C2 | semidirect |
| 11. C2×#3830 | C4 | semidirect |
| 12. C2×D4×C3⋊D3 | C4 | semidirect |
| 15. C32×#117 | C22 | semidirect |
| 16. C2×C32×C22⋊C4 | C22 | semidirect |
| 17. C2×#3757 | C22 | semidirect |
| 19. #64135 | C22 | semidirect |
| 20. #63633 | C22 | semidirect |
| 22. C3×#518 | D3 | semidirect |
| 27. C23×C3⋊D3 | C2×C4 | semidirect |
| 35. C2×#638 | C2×C4 | semidirect |
| 38. C22×C3⋊Dic3 | C2×C4 | semidirect |
| 43. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 44. C2×C4×C3⋊D3 | C2×C4 | semidirect |
| 45. C2×#634 | C2×C4 | semidirect |
| 63. C3×#117 | C2×D3 | semidirect |
| 64. C2×C3×C22⋊C4 | C2×D3 | semidirect |
| 95. #518 | C3⋊D3 | semidirect |
| 151. #117 | C2×C3⋊D3 | semidirect |
| 153. C2×C22⋊C4 | C2×C3⋊D3 | semidirect |
| 228. C32 | #2883 | semidirect |
| 274. C3 | #82546 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64361 | 2 |
| C32×#518 | 2 |
| #10596269 | 2 |
| #10592705 | 2 |
| C2×#63633 | 2 |
| #82546 | 3 |