Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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. #10592382 | C2 | semidirect |
| 4. #10589360 | C2 | semidirect |
| 5. #10589329 | C2 | semidirect |
| 125. C32 | #2231 | semidirect |
| 148. C3 | #70920 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#443 | 2 |
| #10592382 | 2 |
| #10589432 | 2 |
| #10589360 | 2 |
| #10589329 | 2 |
| #70920 | 3 |