Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
684 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 6. C22×C32×C8 | C4 | semidirect |
| 14. #63657 | C4 | semidirect |
| 30. #3757 | C8 | semidirect |
| 36. C22×C3×C8 | Dic3 | semidirect |
| 106. C22×C8 | C3⋊Dic3 | semidirect |
| 177. C32 | #1282 | semidirect |
| 225. C3 | #67677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C22⋊C8 | 2 |
| C4×#3757 | 2 |
| C2×#63657 | 2 |
| #67677 | 3 |