Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
522 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 187 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 |
|---|---|---|
| 3. #10593565 | C2 | semidirect |
| 4. C2×#63748 | C2 | semidirect |
| 5. #10593547 | C2 | semidirect |
| 6. #10593546 | C2 | semidirect |
| 134. C32 | #2916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596640 | 2 |
| C2×#64287 | 2 |
| #10593565 | 2 |
| C2×#63748 | 2 |
| #10593547 | 2 |
| #10593546 | 2 |
| #2916 | 9 |