Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
349 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 349 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 9. #71497 | C3 | direct (N × H) |
| 168. C3×Dic3 | Q32 | semidirect |
| 268. Dic3 | C3×Q32 | semidirect |
| 269. C32 | #2209 | semidirect |
| 305. C3 | #71497 | direct (N × H) |
| 306. C3 | C3×#2209 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q32 | 2 |
| C3×#5183 | 2 |
| C3×Dic3×Q16 | 2 |
| C2×C3×#829 | 2 |
| C3×#4564 | 2 |
| C3×#4503 | 2 |
| C3×Dic3⋊C16 | 2 |
| C3×#2209 | 3 |
| #71497 | 3 |