Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
522 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 106 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×#5713 | C2 | semidirect |
| 3. C3×#4848 | C2 | semidirect |
| 4. C32×#331 | C2 | semidirect |
| 5. C3×#4484 | C2 | semidirect |
| 7. #68402 | C3 | direct (N × H) |
| 20. #5713 | C2×C3 | semidirect |
| 24. #4848 | C2×C3 | semidirect |
| 26. C3×#331 | D3 | semidirect |
| 27. C3×#331 | C2×C3 | semidirect |
| 29. #4484 | C2×C3 | semidirect |
| 91. #331 | C3×D3 | semidirect |
| 237. C32 | #1620 | semidirect |
| 277. C3 | #68402 | direct (N × H) |
| 278. C3 | C3×#1620 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5713 | 2 |
| C3×#5073 | 2 |
| C3×#4848 | 2 |
| C32×#331 | 2 |
| C3×#4484 | 2 |
| C3×#1620 | 3 |
| #68402 | 3 |