Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
339 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 339 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 7. #68588 | C3 | direct (N × H) |
| 80. C32×C8 | Q16 | semidirect |
| 168. C3×C8 | Dic12 | semidirect |
| 169. C3×C8 | C3×Q16 | semidirect |
| 211. C32 | #1674 | semidirect |
| 225. C8 | C3×Dic12 | semidirect |
| 245. C3 | #68588 | direct (N × H) |
| 246. C3 | C3×#1674 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4849 | 2 |
| C3×#4682 | 2 |
| C3×C8×Dic6 | 2 |
| C32×#335 | 2 |
| C3×#4482 | 2 |
| C3×#1674 | 3 |
| #68588 | 3 |