Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
599 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 599 conjugacy classes of subgroups — too many to draw. Only its 148 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. #10591119 | C2 | semidirect |
| 5. #10589171 | C2 | semidirect |
| 259. C32 | #1868 | semidirect |
| 299. C3 | #70002 | semidirect |
| 300. C3 | #72026 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5819 | 2 |
| #10592939 | 2 |
| C3×#5234 | 2 |
| #10591119 | 2 |
| #10589171 | 2 |
| #72026 | 3 |
| #70002 | 3 |