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. #26018884 | C2 | semidirect |
| 4. #26018827 | C2 | semidirect |
| 5. #26018798 | C2 | semidirect |
| 6. #26018725 | C2 | semidirect |
| 7. C89×#1515 | C2 | semidirect |
| 9. #19152314 | C4 | semidirect |
| 11. #19152309 | C4 | semidirect |
| 14. #19152263 | C4 | semidirect |
| 16. #19152251 | C4 | semidirect |
| 274. #1515 | 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 |
|---|---|
| #26034635 | 2 |
| #26018958 | 2 |
| #26018884 | 2 |
| #26018827 | 2 |
| #26018798 | 2 |
| #26018725 | 2 |
| C89×#1515 | 2 |
| #8502 | 89 |