Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
808 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 808 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 |
|---|---|---|
| 3. #26020242 | C2 | semidirect |
| 4. #26020238 | C2 | semidirect |
| 5. #26018371 | C2 | semidirect |
| 6. #26018369 | C2 | semidirect |
| 8. C24×Dic89 | C4 | semidirect |
| 17. #19151473 | C4 | semidirect |
| 19. #19151454 | C4 | semidirect |
| 21. C22⋊C4×Dic89 | C4 | semidirect |
| 127. C24×C89 | C4⋊C4 | semidirect |
| 151. C22⋊C4×C89 | C4⋊C4 | semidirect |
| 267. Dic89 | AΣL(1,𝔽16) | semidirect |
| 286. C89 | #12793 | semidirect |
| 363. C24 | #13083553 | semidirect |
| 427. C22⋊C4 | #13083553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #120×Dic89 | 2 |
| C2×#19151385 | 2 |
| #26020242 | 2 |
| #26020238 | 2 |
| #26018371 | 2 |
| #26018369 | 2 |
| C2×AΣL(1,𝔽16)×C89 | 2 |
| #12793 | 89 |