Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
226 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 52 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. C2×C32×C16 | C4 | semidirect |
| 12. C2×C3⋊(C3⋊C16) | C4 | semidirect |
| 78. C2×C16 | #157 | semidirect |
| 121. C32 | #1383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63770 | 2 |
| C2×#63768 | 2 |
| C2×#63625 | 2 |
| #1383 | 9 |