Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
253 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 253 conjugacy classes of subgroups — too many to draw. Only its 70 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. #67488 | C3 | direct (N × H) |
| 188. C32 | #1350 | semidirect |
| 223. C3 | #67488 | direct (N × H) |
| 224. C3 | C3×#1350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5116 | 2 |
| C32×#341 | 2 |
| C3×#4549 | 2 |
| C3×#1350 | 3 |
| #67488 | 3 |