Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
351 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 351 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. #70962 | C3 | direct (N × H) |
| 220. C32 | #1690 | semidirect |
| 252. C3 | #70962 | direct (N × H) |
| 253. C3 | C3×#1690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#446 | 2 |
| C3×#5020 | 2 |
| C3×#4699 | 2 |
| C3×#4482 | 2 |
| C3×#4457 | 2 |
| C3×#1690 | 3 |
| #70962 | 3 |