Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
509 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 509 conjugacy classes of subgroups — too many to draw. Only its 102 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×#912 | C2 | semidirect |
| 2. C2×C32×D16 | C2 | semidirect |
| 3. C3×#5157 | C2 | semidirect |
| 4. C2×C3×#827 | C2 | semidirect |
| 5. C3×#4562 | C2 | semidirect |
| 6. C3×(C2×D3)⋊C16 | C2 | semidirect |
| 7. C3×#4503 | C2 | semidirect |
| 9. #71468 | C3 | direct (N × H) |
| 26. C2×#912 | C2×C3 | semidirect |
| 29. C2×C3×D16 | D3 | semidirect |
| 30. C2×C3×D16 | C2×C3 | semidirect |
| 32. #5157 | C2×C3 | semidirect |
| 33. C2×#827 | C2×C3 | semidirect |
| 37. #4562 | C2×C3 | semidirect |
| 38. (C2×D3)⋊C16 | C2×C3 | semidirect |
| 39. #4503 | C2×C3 | semidirect |
| 52. C32×D8 | D4 | semidirect |
| 59. C3×Dic12 | D4 | semidirect |
| 122. C2×D16 | C3×D3 | semidirect |
| 160. C3×D8 | #67 | semidirect |
| 161. C3×D8 | C3×D4 | semidirect |
| 175. Dic12 | C3×D4 | semidirect |
| 285. D8 | C3×#67 | semidirect |
| 333. C32 | #2186 | semidirect |
| 388. C3 | #71468 | direct (N × H) |
| 389. C3 | C3×#2186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#912 | 2 |
| C2×C32×D16 | 2 |
| C3×#5157 | 2 |
| C2×C3×#827 | 2 |
| C3×#4562 | 2 |
| C3×(C2×D3)⋊C16 | 2 |
| C3×#4503 | 2 |
| C3×#2186 | 3 |
| #71468 | 3 |