Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
337 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 337 conjugacy classes of subgroups — too many to draw. Only its 130 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. #71496 | C3 | direct (N × H) |
| 10. C32×Q32 | C4 | semidirect |
| 45. C3×Q32 | Dic3 | semidirect |
| 46. C3×Q32 | C3×C4 | semidirect |
| 107. Q32 | C3×Dic3 | semidirect |
| 166. C32 | #2176 | semidirect |
| 189. C3 | #71496 | direct (N × H) |
| 190. C3 | C3×#2176 | 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×Dic3×Q16 | 2 |
| C3×#4564 | 2 |
| C3×#4505 | 2 |
| C3×#4502 | 2 |
| C3×#2176 | 3 |
| #71496 | 3 |