Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
226 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 8. #63770 | C4 | semidirect |
| 11. C32×M32 | C4 | semidirect |
| 12. #63639 | C4 | semidirect |
| 78. M32 | #157 | semidirect |
| 124. C32 | #1387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593771 | 2 |
| C2×#63769 | 2 |
| C3⋊D3×M32 | 2 |
| #1387 | 9 |