Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
230 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 7. #63773 | C4 | semidirect |
| 12. C32×M32 | C4 | semidirect |
| 13. #63639 | C4 | semidirect |
| 81. M32 | #157 | semidirect |
| 125. C32 | #1377 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63767 | 2 |
| #10593762 | 2 |
| C3⋊D3×M32 | 2 |
| #1377 | 9 |