Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
307 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 307 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 4. C2×#63551 | C2 | semidirect |
| 5. #10589383 | C2 | semidirect |
| 6. C3×#4517 | C2 | semidirect |
| 7. #10589143 | C2 | semidirect |
| 37. #4517 | D3 | semidirect |
| 265. C32 | #2222 | semidirect |
| 298. C3 | #69270 | semidirect |
| 299. C3 | #71456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4907 | 2 |
| #10590932 | 2 |
| #10590930 | 2 |
| C2×#63551 | 2 |
| #10589383 | 2 |
| C3×#4517 | 2 |
| #10589143 | 2 |
| #71456 | 3 |
| #69270 | 3 |