Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
726 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 3. #26018582 | C2 | semidirect |
| 4. #26018105 | C2 | semidirect |
| 5. C89×#2313 | C2 | semidirect |
| 10. #19151518 | C4 | semidirect |
| 11. #19151515 | C4 | semidirect |
| 172. #2313 | D89 | semidirect |
| 176. C89 | #9480 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023587 | 2 |
| #26020197 | 2 |
| #26018582 | 2 |
| #26018105 | 2 |
| C89×#2313 | 2 |
| #9480 | 89 |