Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
156 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 156 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. Q82×C89 | C4 | semidirect |
| 9. #333×C89 | C4 | semidirect |
| 77. C89 | #7520 | semidirect |
| 78. Q82 | Dic89 | semidirect |
| 83. #333 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018417 | 2 |
| #26018293 | 2 |
| C89×#1623 | 2 |
| #7520 | 89 |