Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
508 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26019969 | C2 | semidirect |
| 3. #26018262 | C2 | semidirect |
| 4. C89×#2112 | C2 | semidirect |
| 5. C22×D712 | C4 | semidirect |
| 10. #19151834 | C4 | semidirect |
| 12. C2×#15667946 | C4 | semidirect |
| 15. #19151361 | C22 | semidirect |
| 19. C22⋊C16×C89 | C22 | semidirect |
| 158. #2112 | D89 | semidirect |
| 161. C89 | #11705 | semidirect |
| 174. C22⋊C16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151834 | 2 |
| #26019969 | 2 |
| #26018262 | 2 |
| C89×#2112 | 2 |
| #11705 | 89 |