Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
5904 conjugacy classes of subgroups; only the 1321 normal subgroups are shown.
This group has 5904 conjugacy classes of subgroups — too many to draw. Only its 1321 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. C24×C32×C4 | C2 | semidirect |
| 3. C22×#3757 | C2 | semidirect |
| 4. C2×#64138 | C2 | direct (N × H) |
| 5. C22×#3752 | C2 | semidirect |
| 6. C22×#3750 | C2 | semidirect |
| 12. C23×C32×C4 | C22 | semidirect |
| 17. C2×#3757 | C22 | semidirect |
| 18. #64138 | C22 | direct (N × H) |
| 19. C2×#3752 | C22 | semidirect |
| 20. C2×#3750 | C22 | semidirect |
| 21. C24×C3×C4 | D3 | semidirect |
| 37. C22×C32×C4 | C23 | semidirect |
| 44. #3757 | C23 | semidirect |
| 45. #3752 | C23 | semidirect |
| 46. #3750 | C23 | semidirect |
| 52. C23×C3×C4 | C2×D3 | semidirect |
| 81. C24×C4 | C3⋊D3 | semidirect |
| 96. C22×C3×C4 | C22×D3 | semidirect |
| 108. C22×C32 | #123 | semidirect |
| 127. C23×C4 | C2×C3⋊D3 | semidirect |
| 152. C2×C32 | C2×#123 | semidirect |
| 172. C22×C4 | C22×C3⋊D3 | semidirect |
| 178. C22×C3 | #929 | semidirect |
| 189. C32 | C22×#123 | semidirect |
| 210. C2×C3 | C2×#929 | semidirect |
| 219. C22 | #64138 | direct (N × H) |
| 227. C3 | C22×#929 | semidirect |
| 230. C2 | C2×#64138 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C32×C4 | 2 |
| C23×#638 | 2 |
| C22×#3757 | 2 |
| C2×#64138 | 2 |
| C22×#3752 | 2 |
| C22×#3750 | 2 |
| C22×#929 | 3 |