Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
497 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 497 conjugacy classes of subgroups — too many to draw. Only its 106 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×C3×D3×Q16 | C2 | semidirect |
| 2. C2×C32×SD32 | C2 | semidirect |
| 4. C2×C3×#827 | C2 | semidirect |
| 5. C3×#4564 | C2 | semidirect |
| 6. C3×(C2×D3)⋊C16 | C2 | semidirect |
| 7. C3×#4503 | C2 | semidirect |
| 9. #71483 | C3 | direct (N × H) |
| 26. C2×D3×Q16 | C2×C3 | semidirect |
| 29. C2×C3×SD32 | D3 | semidirect |
| 30. C2×C3×SD32 | C2×C3 | semidirect |
| 33. C2×#827 | C2×C3 | semidirect |
| 37. #4564 | C2×C3 | semidirect |
| 38. (C2×D3)⋊C16 | C2×C3 | semidirect |
| 39. #4503 | C2×C3 | semidirect |
| 50. C32×Q16 | D4 | semidirect |
| 59. C3×Dic12 | D4 | semidirect |
| 122. C2×SD32 | C3×D3 | semidirect |
| 154. C3×Q16 | #67 | semidirect |
| 155. C3×Q16 | C3×D4 | semidirect |
| 175. Dic12 | C3×D4 | semidirect |
| 189. C2×C3×D3 | SD32 | semidirect |
| 280. Q16 | C3×#67 | semidirect |
| 308. C2×D3 | C3×SD32 | semidirect |
| 324. C32 | #2185 | semidirect |
| 374. C3 | #71483 | direct (N × H) |
| 375. C3 | C3×#2185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×Q16 | 2 |
| C2×C32×SD32 | 2 |
| C3×#5157 | 2 |
| C2×C3×#827 | 2 |
| C3×#4564 | 2 |
| C3×(C2×D3)⋊C16 | 2 |
| C3×#4503 | 2 |
| C3×#2185 | 3 |
| #71483 | 3 |