Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
372 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26022488 | C2 | semidirect |
| 3. #26022400 | C2 | semidirect |
| 4. #26019766 | C2 | semidirect |
| 5. #26018218 | C2 | semidirect |
| 6. #26018209 | C2 | semidirect |
| 7. C89×#1360 | C2 | semidirect |
| 10. #19152003 | C22 | semidirect |
| 22. #19151374 | C22 | semidirect |
| 25. C4⋊C16×C89 | C22 | semidirect |
| 26. #334×C89 | C22 | semidirect |
| 79. D712 | SD16 | semidirect |
| 171. #1360 | D89 | semidirect |
| 174. C89 | #12378 | semidirect |
| 187. C4⋊C16 | C2×D89 | semidirect |
| 192. #334 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031861 | 2 |
| #26022488 | 2 |
| #26022400 | 2 |
| #26019766 | 2 |
| #26018218 | 2 |
| #26018209 | 2 |
| C89×#1360 | 2 |
| #12378 | 89 |