Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26022053 | C2 | semidirect |
| 3. #26022050 | C2 | semidirect |
| 4. #26018211 | C2 | semidirect |
| 5. #26018210 | C2 | semidirect |
| 6. #26018209 | C2 | semidirect |
| 7. C89×#1330 | C2 | semidirect |
| 18. C4⋊#13083549 | C22 | semidirect |
| 22. #19151374 | C22 | semidirect |
| 25. C4⋊C16×C89 | C22 | semidirect |
| 26. #346×C89 | C22 | semidirect |
| 176. #1330 | D89 | semidirect |
| 177. C89 | #11634 | semidirect |
| 191. C4⋊C16 | C2×D89 | semidirect |
| 195. #346 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #436×D89 | 2 |
| #26022053 | 2 |
| #26022050 | 2 |
| #26018211 | 2 |
| #26018210 | 2 |
| #26018209 | 2 |
| C89×#1330 | 2 |
| #11634 | 89 |