Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
333 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 333 conjugacy classes of subgroups — too many to draw. Only its 110 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. #69293 | C3 | direct (N × H) |
| 124. C32×C4 | Q32 | semidirect |
| 203. C3×C4 | Dic24 | semidirect |
| 204. C3×C4 | C3×Q32 | semidirect |
| 212. C32 | #2209 | semidirect |
| 240. C4 | C3×Dic24 | semidirect |
| 244. C3 | #69293 | direct (N × H) |
| 245. C3 | C3×#2209 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic24 | 2 |
| C3×#4699 | 2 |
| C3×C4×Dic12 | 2 |
| C32×C4⋊C16 | 2 |
| C3×#4503 | 2 |
| C3×#2209 | 3 |
| #69293 | 3 |