Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
134 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 27 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 |
|---|---|---|
| 6. #564×C89 | C4 | semidirect |
| 10. #330×C89 | C4 | semidirect |
| 68. C89 | #7524 | semidirect |
| 69. #564 | Dic89 | semidirect |
| 75. #330 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018423 | 2 |
| #26018285 | 2 |
| C89×#1658 | 2 |
| #7524 | 89 |