Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
582 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26020239 | C2 | semidirect |
| 3. #26018587 | C2 | semidirect |
| 4. #26018277 | C2 | semidirect |
| 5. #26018275 | C2 | semidirect |
| 6. #26018249 | C2 | semidirect |
| 7. C89×#1343 | C2 | semidirect |
| 9. C2×D4×Dic89 | C4 | semidirect |
| 14. #19151535 | C4 | semidirect |
| 18. #19151506 | C4 | semidirect |
| 20. #19151443 | C4 | semidirect |
| 235. #1343 | D89 | semidirect |
| 236. C89 | #11821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023530 | 2 |
| #26020239 | 2 |
| #26018587 | 2 |
| #26018277 | 2 |
| #26018275 | 2 |
| #26018249 | 2 |
| C89×#1343 | 2 |
| #11821 | 89 |