Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
255 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 255 conjugacy classes of subgroups — too many to draw. Only its 66 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. #67781 | C3 | direct (N × H) |
| 193. C32 | #1342 | semidirect |
| 224. C3 | #67781 | direct (N × H) |
| 225. C3 | C3×#1342 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#470 | 2 |
| C3×C3⋊#338 | 2 |
| C3×#4553 | 2 |
| C3×#1342 | 3 |
| #67781 | 3 |