Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
242 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 4. #10590137 | C2 | semidirect |
| 12. C32×M32 | C4 | semidirect |
| 13. #63639 | C4 | semidirect |
| 15. C16×C3⋊D3 | C4 | semidirect |
| 30. C32×C16 | C2×C4 | semidirect |
| 31. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 79. M32 | #157 | semidirect |
| 99. C3⋊D3 | #365 | semidirect |
| 114. C16 | C2×#157 | semidirect |
| 123. C32 | C2×#365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593771 | 2 |
| C2×#63768 | 2 |
| C3⋊D3×M32 | 2 |
| #10590137 | 2 |
| C2×#365 | 9 |