Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
417 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 417 conjugacy classes of subgroups — too many to draw. Only its 134 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. #70626 | C3 | direct (N × H) |
| 216. C32 | #2089 | semidirect |
| 252. C3 | #70626 | direct (N × H) |
| 253. C3 | C3×#2089 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#107 | 2 |
| C3×#5102 | 2 |
| C3×#4964 | 2 |
| C3×#4552 | 2 |
| C3×#4530 | 2 |
| C3×#2089 | 3 |
| #70626 | 3 |