Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
605 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 605 conjugacy classes of subgroups — too many to draw. Only its 178 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. #71659 | C3 | direct (N × H) |
| 160. C32 | #1830 | semidirect |
| 185. C3 | #71659 | direct (N × H) |
| 186. C3 | C3×#1830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#519 | 2 |
| C2×C3×#836 | 2 |
| C3×#4533 | 2 |
| C3×#1830 | 3 |
| #71659 | 3 |