Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
323 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 323 conjugacy classes of subgroups — too many to draw. Only its 122 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. #69082 | C3 | direct (N × H) |
| 15. C3×Dic24 | C4 | semidirect |
| 57. Dic24 | C3×C4 | semidirect |
| 165. C32 | #2176 | semidirect |
| 188. C3 | #69082 | direct (N × H) |
| 189. C3 | C3×#2176 | 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×C4×Dic12 | 2 |
| C32×#346 | 2 |
| C3×#4505 | 2 |
| C3×#4503 | 2 |
| C3×#2176 | 3 |
| #69082 | 3 |