Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
372 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 98 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. C3×#5088 | C2 | semidirect |
| 2. C3×#5084 | C2 | semidirect |
| 4. C3×#4838 | C2 | semidirect |
| 5. C32×#333 | C2 | semidirect |
| 6. C3×#4485 | C2 | semidirect |
| 7. C3×#4479 | C2 | semidirect |
| 9. #68502 | C3 | direct (N × H) |
| 29. #5088 | C2×C3 | semidirect |
| 30. #5084 | C2×C3 | semidirect |
| 32. #4838 | C2×C3 | semidirect |
| 35. C3×#333 | D3 | semidirect |
| 36. C3×#333 | C2×C3 | semidirect |
| 38. #4485 | C2×C3 | semidirect |
| 39. #4479 | C2×C3 | semidirect |
| 119. #333 | C3×D3 | semidirect |
| 301. C32 | #1697 | semidirect |
| 352. C3 | #68502 | direct (N × H) |
| 353. C3 | C3×#1697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5088 | 2 |
| C3×#5084 | 2 |
| C3×#4843 | 2 |
| C3×#4838 | 2 |
| C32×#333 | 2 |
| C3×#4485 | 2 |
| C3×#4479 | 2 |
| C3×#1697 | 3 |
| #68502 | 3 |