Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
279 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 279 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 |
|---|---|---|
| 2. C32×#347 | C2 | semidirect |
| 4. C3×#4511 | C2 | semidirect |
| 5. C3×#4466 | C2 | semidirect |
| 7. #69088 | C3 | direct (N × H) |
| 23. C3×#347 | D3 | semidirect |
| 24. C3×#347 | C2×C3 | semidirect |
| 26. #4511 | C2×C3 | semidirect |
| 27. #4466 | C2×C3 | semidirect |
| 78. #347 | C3×D3 | semidirect |
| 190. C32 | #2165 | semidirect |
| 220. C3 | #69088 | direct (N × H) |
| 221. C3 | C3×#2165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4707 | 2 |
| C32×#347 | 2 |
| C3×#4514 | 2 |
| C3×#4511 | 2 |
| C3×#4466 | 2 |
| C3×#2165 | 3 |
| #69088 | 3 |