Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
13209 conjugacy classes of subgroups; only the 4100 normal subgroups are shown.
This group has 13209 conjugacy classes of subgroups — too many to draw. Only its 4100 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. C23×C3×Dic6 | C2 | semidirect |
| 3. C23×#627 | C2 | semidirect |
| 5. C22×#3797 | C2 | direct (N × H) |
| 12. C22×C3×Dic6 | C22 | semidirect |
| 13. C22×#627 | C22 | semidirect |
| 15. C2×#3797 | C22 | direct (N × H) |
| 22. C23×Dic6 | D3 | semidirect |
| 24. C23×C3⋊D3 | Q8 | semidirect |
| 30. C2×C3×Dic6 | C23 | semidirect |
| 31. C2×#627 | C23 | semidirect |
| 33. #3797 | C23 | direct (N × H) |
| 49. C22×Dic6 | C2×D3 | semidirect |
| 50. C23×C32 | C2×Q8 | semidirect |
| 52. C22×C3⋊D3 | C2×Q8 | semidirect |
| 58. C3×Dic6 | C24 | semidirect |
| 59. #627 | C24 | semidirect |
| 84. C2×Dic6 | C22×D3 | semidirect |
| 85. C22×C32 | C22×Q8 | semidirect |
| 87. C2×C3⋊D3 | C22×Q8 | semidirect |
| 103. C23×C3 | D3×Q8 | semidirect |
| 120. Dic6 | C23×D3 | semidirect |
| 121. C2×C32 | C23×Q8 | semidirect |
| 123. C3⋊D3 | C23×Q8 | semidirect |
| 137. C22×C3 | C2×D3×Q8 | semidirect |
| 149. C32 | C24×Q8 | semidirect |
| 152. C23 | #3797 | direct (N × H) |
| 163. C2×C3 | C22×D3×Q8 | semidirect |
| 169. C22 | C2×#3797 | direct (N × H) |
| 175. C3 | C23×D3×Q8 | semidirect |
| 177. C2 | C22×#3797 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C3⋊D3 | 2 |
| C23×C3×Dic6 | 2 |
| C23×#627 | 2 |
| C23×#624 | 2 |
| C22×#3797 | 2 |
| C23×D3×Q8 | 3 |