Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
480 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 149 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. #10592379 | C2 | semidirect |
| 5. #10589352 | C2 | semidirect |
| 6. #10589347 | C2 | semidirect |
| 7. #10589324 | C2 | semidirect |
| 81. C32×C8 | SD16 | semidirect |
| 152. C3×C8 | #214 | semidirect |
| 189. C32 | #1691 | semidirect |
| 208. C8 | #3754 | semidirect |
| 225. C3 | #70872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#436 | 2 |
| #10592718 | 2 |
| #10592707 | 2 |
| #10592379 | 2 |
| #10589352 | 2 |
| #10589347 | 2 |
| #10589324 | 2 |
| #70872 | 3 |