Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
389 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 389 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 |
|---|---|---|
| 2. C3×#5155 | C2 | semidirect |
| 3. C3×Dic3×D8 | C2 | semidirect |
| 4. C2×C3×#827 | C2 | semidirect |
| 5. C3×#4562 | C2 | semidirect |
| 6. C3×#4503 | C2 | semidirect |
| 7. C3×Dic3⋊C16 | C2 | semidirect |
| 9. #71463 | C3 | direct (N × H) |
| 29. #5155 | C2×C3 | semidirect |
| 30. Dic3×D8 | C2×C3 | semidirect |
| 31. C2×#827 | C2×C3 | semidirect |
| 35. #4562 | C2×C3 | semidirect |
| 36. #4503 | C2×C3 | semidirect |
| 37. Dic3⋊C16 | C2×C3 | semidirect |
| 290. C32 | #2210 | semidirect |
| 337. C3 | #71463 | direct (N × H) |
| 338. C3 | C3×#2210 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D16 | 2 |
| C3×#5155 | 2 |
| C3×Dic3×D8 | 2 |
| C2×C3×#827 | 2 |
| C3×#4562 | 2 |
| C3×#4503 | 2 |
| C3×Dic3⋊C16 | 2 |
| C3×#2210 | 3 |
| #71463 | 3 |