Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
316 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 70 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×#4897 | C2 | semidirect |
| 2. #10590926 | C2 | semidirect |
| 3. C2×#63545 | C2 | semidirect |
| 4. #10590622 | C2 | semidirect |
| 5. #10589359 | C2 | semidirect |
| 6. C3×#4495 | C2 | semidirect |
| 7. #10589127 | C2 | semidirect |
| 32. #4897 | D3 | semidirect |
| 36. #4495 | D3 | semidirect |
| 269. C32 | #2221 | semidirect |
| 308. C3 | #69260 | semidirect |
| 309. C3 | #71092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4897 | 2 |
| #10590926 | 2 |
| C2×#63545 | 2 |
| #10590622 | 2 |
| #10589359 | 2 |
| C3×#4495 | 2 |
| #10589127 | 2 |
| #71092 | 3 |
| #69260 | 3 |