Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
564 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 141 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. #10592774 | C2 | semidirect |
| 3. C8×#634 | C2 | semidirect |
| 4. #10589410 | C2 | semidirect |
| 5. #10589324 | C2 | semidirect |
| 62. #634 | D8 | semidirect |
| 64. C32×C8 | SD16 | semidirect |
| 123. C3×C8 | #214 | semidirect |
| 156. C32 | #1668 | semidirect |
| 173. C8 | #3754 | semidirect |
| 189. C3 | #71286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#493 | 2 |
| #10592774 | 2 |
| C8×#634 | 2 |
| #10589410 | 2 |
| #10589324 | 2 |
| #71286 | 3 |