Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
300 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 300 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 |
|---|---|---|
| 3. C2×#63550 | C2 | semidirect |
| 5. #10589359 | C2 | semidirect |
| 6. C3×#4496 | C2 | semidirect |
| 7. #10589130 | C2 | semidirect |
| 36. #4496 | D3 | semidirect |
| 261. C32 | #2222 | semidirect |
| 294. C3 | #69270 | semidirect |
| 295. C3 | #71096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4896 | 2 |
| #10590930 | 2 |
| C2×#63550 | 2 |
| #10590622 | 2 |
| #10589359 | 2 |
| C3×#4496 | 2 |
| #10589130 | 2 |
| #71096 | 3 |
| #69270 | 3 |