Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
508 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26021861 | C2 | semidirect |
| 3. #26019967 | C2 | semidirect |
| 4. #26018262 | C2 | semidirect |
| 5. #26018261 | C2 | semidirect |
| 6. #26018260 | C2 | semidirect |
| 7. C89×#1347 | C2 | semidirect |
| 8. C2×D8×D89 | C4 | semidirect |
| 13. #19151835 | C4 | semidirect |
| 17. #19151831 | C4 | semidirect |
| 18. #107×D89 | C4 | semidirect |
| 20. C22⋊#13083549 | C22 | semidirect |
| 22. #19151361 | C22 | semidirect |
| 25. C22⋊C16×C89 | C22 | semidirect |
| 26. #340×C89 | C22 | semidirect |
| 211. #1347 | D89 | semidirect |
| 212. C89 | #11705 | semidirect |
| 228. C22⋊C16 | C2×D89 | semidirect |
| 231. #340 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #466×D89 | 2 |
| #26021861 | 2 |
| #26019967 | 2 |
| #26018262 | 2 |
| #26018261 | 2 |
| #26018260 | 2 |
| C89×#1347 | 2 |
| #11705 | 89 |