Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
247 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 247 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 2. #10589329 | C2 | semidirect |
| 3. C3×#4463 | C2 | semidirect |
| 18. #4463 | D3 | semidirect |
| 152. C32 | #1357 | semidirect |
| 178. C3 | #67571 | semidirect |
| 179. C3 | #67791 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4695 | 2 |
| #10589329 | 2 |
| C3×#4463 | 2 |
| #67791 | 3 |
| #67571 | 3 |