Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
341 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 76 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. C2×C3×Dic24 | C2 | semidirect |
| 3. #10590818 | C2 | semidirect |
| 5. #10589367 | C2 | semidirect |
| 7. #10589117 | C2 | semidirect |
| 29. C2×Dic24 | D3 | semidirect |
| 269. C32 | #2211 | semidirect |
| 309. C3 | #69205 | semidirect |
| 310. C3 | #71498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic24 | 2 |
| #10590869 | 2 |
| #10590818 | 2 |
| C2×#63547 | 2 |
| #10589367 | 2 |
| C3×#4509 | 2 |
| #10589117 | 2 |
| #71498 | 3 |
| #69205 | 3 |