Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
341 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 11. #63628 | C4 | semidirect |
| 106. C3×Dic3 | Q32 | semidirect |
| 172. Dic3 | Dic24 | semidirect |
| 173. C32 | C4×Q32 | semidirect |
| 201. C3 | C4×Dic24 | semidirect |
| 202. C3 | #69318 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63628 | 2 |
| #10590807 | 2 |
| C3×#4504 | 2 |
| C3×Dic3×C16 | 2 |
| #10589119 | 2 |
| #69318 | 3 |
| C4×Dic24 | 3 |