Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
672 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 672 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 |
|---|---|---|
| 2. #26018958 | C2 | semidirect |
| 3. #26018829 | C2 | semidirect |
| 4. #26018804 | C2 | semidirect |
| 5. #26018800 | C2 | semidirect |
| 6. #26018724 | C2 | semidirect |
| 7. C89×#1535 | C2 | semidirect |
| 10. #19152313 | C4 | semidirect |
| 11. #19152308 | C4 | semidirect |
| 14. Q8×D356 | C4 | semidirect |
| 16. #19152252 | C4 | semidirect |
| 272. #1535 | D89 | semidirect |
| 277. C89 | #8502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034643 | 2 |
| #26018958 | 2 |
| #26018829 | 2 |
| #26018804 | 2 |
| #26018800 | 2 |
| #26018724 | 2 |
| C89×#1535 | 2 |
| #8502 | 89 |