Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
199 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 199 conjugacy classes of subgroups — too many to draw. Only its 82 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. #67518 | C3 | direct (N × H) |
| 156. C32 | #1338 | semidirect |
| 184. C3 | #67518 | direct (N × H) |
| 185. C3 | C3×#1338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4679 | 2 |
| C32×#346 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| C3×#1338 | 3 |
| #67518 | 3 |