Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
225 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 225 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 5. #67505 | C3 | direct (N × H) |
| 29. C3×Dic12 | C8 | semidirect |
| 84. Dic12 | C3×C8 | semidirect |
| 167. C32 | #1332 | semidirect |
| 197. C3 | #67505 | direct (N × H) |
| 198. C3 | C3×#1332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×Dic12 | 2 |
| C32×C4×C16 | 2 |
| C3×#4458 | 2 |
| C3×#1332 | 3 |
| #67505 | 3 |