Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
475 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 475 conjugacy classes of subgroups — too many to draw. Only its 114 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×#486 | C2 | semidirect |
| 2. C3×#5088 | C2 | semidirect |
| 3. C3×#5079 | C2 | semidirect |
| 4. C3×#5076 | C2 | semidirect |
| 6. C3×#4694 | C2 | semidirect |
| 7. C3×#4455 | C2 | semidirect |
| 9. #71187 | C3 | direct (N × H) |
| 29. C3×#486 | D3 | semidirect |
| 30. C3×#486 | C2×C3 | semidirect |
| 31. #5088 | C2×C3 | semidirect |
| 32. #5079 | C2×C3 | semidirect |
| 33. #5076 | C2×C3 | semidirect |
| 35. #4694 | C2×C3 | semidirect |
| 37. #4455 | C2×C3 | semidirect |
| 110. #486 | C3×D3 | semidirect |
| 282. C32 | #1717 | semidirect |
| 328. C3 | #71187 | direct (N × H) |
| 329. C3 | C3×#1717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#486 | 2 |
| C3×#5088 | 2 |
| C3×#5079 | 2 |
| C3×#5076 | 2 |
| C3×#5073 | 2 |
| C3×#4694 | 2 |
| C3×#4455 | 2 |
| C3×#1717 | 3 |
| #71187 | 3 |