Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
261 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 86 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×#4858 | C2 | semidirect |
| 3. C32×#365 | C2 | semidirect |
| 5. C3×#4511 | C2 | semidirect |
| 6. C3×#4494 | C2 | semidirect |
| 9. #69316 | C3 | direct (N × H) |
| 24. #4858 | C2×C3 | semidirect |
| 27. C3×#365 | D3 | semidirect |
| 28. C3×#365 | C2×C3 | semidirect |
| 33. #4511 | C2×C3 | semidirect |
| 34. #4494 | C2×C3 | semidirect |
| 94. #365 | C3×D3 | semidirect |
| 223. C32 | #2231 | semidirect |
| 254. C3 | #69316 | direct (N × H) |
| 255. C3 | C3×#2231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4895 | 2 |
| C3×#4858 | 2 |
| C32×#365 | 2 |
| C3×#4518 | 2 |
| C3×#4511 | 2 |
| C3×#4494 | 2 |
| C3×#4488 | 2 |
| C3×#2231 | 3 |
| #69316 | 3 |