Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
552 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 289 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. #10589368 | C2 | semidirect |
| 5. C16×C3⋊Dic3 | C2 | semidirect |
| 10. C32×M32 | C4 | semidirect |
| 14. C2×C3⋊(C3⋊C16) | C4 | semidirect |
| 39. C3×M32 | Dic3 | semidirect |
| 84. M32 | C3⋊Dic3 | semidirect |
| 124. C32 | #2108 | semidirect |
| 145. C3 | #71419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×M32 | 2 |
| #10592800 | 2 |
| C22×C3⋊(C3⋊C16) | 2 |
| #10589368 | 2 |
| C16×C3⋊Dic3 | 2 |
| #71419 | 3 |