Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1897 conjugacy classes of subgroups; only the 458 normal subgroups are shown.
This group has 1897 conjugacy classes of subgroups — too many to draw. Only its 458 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 |
|---|---|---|
| 4. #72134 | C3 | direct (N × H) |
| 6. C22×C32×Q8 | C4 | semidirect |
| 23. C22×C3×Dic3 | Q8 | semidirect |
| 29. C22×C3×Q8 | Dic3 | semidirect |
| 30. C22×C3×Q8 | C3×C4 | semidirect |
| 74. C22×Dic3 | C3×Q8 | semidirect |
| 84. C22×Q8 | C3×Dic3 | semidirect |
| 154. C32 | #1446 | semidirect |
| 187. C3 | #72134 | direct (N × H) |
| 188. C3 | C3×#1446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32×Q8 | 2 |
| C2×C3×C3⋊#95 | 2 |
| C3×#1446 | 3 |
| #72134 | 3 |