Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
350 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 94 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. C32×#472 | C2 | semidirect |
| 2. C2×C3×#826 | C2 | semidirect |
| 3. C3×#5142 | C2 | semidirect |
| 4. C3×#5140 | C2 | semidirect |
| 5. C3×#4563 | C2 | semidirect |
| 6. C3×#4495 | C2 | semidirect |
| 7. C3×#4493 | C2 | semidirect |
| 9. #71092 | C3 | direct (N × H) |
| 29. C3×#472 | D3 | semidirect |
| 30. C3×#472 | C2×C3 | semidirect |
| 31. C2×#826 | C2×C3 | semidirect |
| 32. #5142 | C2×C3 | semidirect |
| 33. #5140 | C2×C3 | semidirect |
| 37. #4563 | C2×C3 | semidirect |
| 38. #4495 | C2×C3 | semidirect |
| 39. #4493 | C2×C3 | semidirect |
| 115. #472 | C3×D3 | semidirect |
| 288. C32 | #2221 | semidirect |
| 329. C3 | #71092 | direct (N × H) |
| 330. C3 | C3×#2221 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#472 | 2 |
| C2×C3×#826 | 2 |
| C3×#5142 | 2 |
| C3×#5140 | 2 |
| C3×#4563 | 2 |
| C3×#4495 | 2 |
| C3×#4493 | 2 |
| C3×#2221 | 3 |
| #71092 | 3 |