Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
365 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 365 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. #71309 | C3 | direct (N × H) |
| 217. C32 | #1690 | semidirect |
| 249. C3 | #71309 | direct (N × H) |
| 250. C3 | C3×#1690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#494 | 2 |
| C3×#5094 | 2 |
| C3×#4679 | 2 |
| C3×#4547 | 2 |
| C3×#4457 | 2 |
| C3×#1690 | 3 |
| #71309 | 3 |