Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
315 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 315 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. #68589 | C3 | direct (N × H) |
| 204. C32 | #1676 | semidirect |
| 237. C3 | #68589 | direct (N × H) |
| 238. C3 | C3×#1676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4850 | 2 |
| C3×#4682 | 2 |
| C3×C8×Dic6 | 2 |
| C32×#335 | 2 |
| C3×#4481 | 2 |
| C3×#1676 | 3 |
| #68589 | 3 |