Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1252 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 1. #26030705 | C2 | semidirect |
| 2. #26019541 | C2 | semidirect |
| 3. #26018844 | C2 | semidirect |
| 4. C89×#3549 | C2 | semidirect |
| 6. C2×#15668009 | C22 | semidirect |
| 7. #19151988 | C22 | semidirect |
| 10. C4×#13083558 | C22 | semidirect |
| 11. #19151338 | C22 | semidirect |
| 12. H(3,𝔽4)×C89 | C22 | semidirect |
| 97. #3549 | D89 | semidirect |
| 101. C89 | #19073 | semidirect |
| 103. H(3,𝔽4) | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030705 | 2 |
| #26019541 | 2 |
| #26018844 | 2 |
| C89×#3549 | 2 |
| #19073 | 89 |