Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
782 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 218 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 |
|---|---|---|
| 1. C2×D4×C92 | C2 | semidirect |
| 2. #13047416 | C2 | semidirect |
| 3. #13046806 | C2 | semidirect |
| 4. #13046805 | C2 | semidirect |
| 5. #13046764 | C2 | semidirect |
| 12. C4⋊(C9⋊D9) | C22 | semidirect |
| 14. #10619651 | C22 | semidirect |
| 15. C9⋊(C9⋊C8) | C22 | semidirect |
| 48. C2×D4×C9 | D9 | semidirect |
| 61. C92 | AGL(1,ℤ/8) | semidirect |
| 123. C2×D4 | C9⋊D9 | semidirect |
| 135. C9 | #63495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C92 | 2 |
| #13047416 | 2 |
| #13046806 | 2 |
| #13046805 | 2 |
| #13046764 | 2 |
| #11721833 | 3 |