Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
462 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #26023053 | C2 | semidirect |
| 4. #26018853 | C2 | semidirect |
| 6. #26018107 | C2 | semidirect |
| 7. C89×#1288 | C2 | semidirect |
| 10. #19152007 | C4 | semidirect |
| 11. #19151963 | C4 | semidirect |
| 203. #1288 | D89 | semidirect |
| 205. C89 | #9382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031444 | 2 |
| #26023053 | 2 |
| #26021171 | 2 |
| #26018853 | 2 |
| #26018798 | 2 |
| #26018107 | 2 |
| C89×#1288 | 2 |
| #9382 | 89 |