Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
138 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 138 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. #498×C89 | C4 | semidirect |
| 10. C82×C89 | C4 | semidirect |
| 63. C89 | #7536 | semidirect |
| 64. #498 | Dic89 | semidirect |
| 70. C82 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018419 | 2 |
| #26018417 | 2 |
| C89×#1708 | 2 |
| #7536 | 89 |