Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1365 conjugacy classes of subgroups; only the 346 normal subgroups are shown.
This group has 1365 conjugacy classes of subgroups — too many to draw. Only its 346 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×#383 | C2 | semidirect |
| 3. C3×#4937 | C2 | semidirect |
| 4. C3×#4665 | C2 | semidirect |
| 6. #74298 | C3 | direct (N × H) |
| 11. C3×#874 | C4 | semidirect |
| 19. C3×#383 | D3 | semidirect |
| 20. C3×#383 | C2×C3 | semidirect |
| 21. #4937 | C2×C3 | semidirect |
| 22. #4665 | C2×C3 | semidirect |
| 29. C2×C3×D12 | C2×C4 | semidirect |
| 31. C32×C42 | C2×C4 | semidirect |
| 44. #874 | C3×C4 | semidirect |
| 63. #383 | C3×D3 | semidirect |
| 80. C2×D12 | C2×C3×C4 | semidirect |
| 84. C3×C42 | C4×D3 | semidirect |
| 85. C3×C42 | C2×C3×C4 | semidirect |
| 138. C42 | C3×C4×D3 | semidirect |
| 159. C32 | #2380 | semidirect |
| 187. C3 | #74298 | direct (N × H) |
| 188. C3 | C3×#2380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#874 | 2 |
| C32×#383 | 2 |
| C3×#4937 | 2 |
| C3×#4665 | 2 |
| C3×#2380 | 3 |
| #74298 | 3 |