Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1054 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 1054 conjugacy classes of subgroups — too many to draw. Only its 143 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. #26021047 | C2 | semidirect |
| 3. #26018930 | C2 | semidirect |
| 4. #26018702 | C2 | semidirect |
| 5. C89×#1800 | C2 | semidirect |
| 14. C2×C4⋊#10623494 | C22 | semidirect |
| 16. C2×C4×#10623494 | C22 | semidirect |
| 21. #423×C89 | C22 | semidirect |
| 194. #1800 | D89 | semidirect |
| 197. C89 | #8353 | semidirect |
| 207. #423 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034016 | 2 |
| #26021047 | 2 |
| #26018930 | 2 |
| #26018702 | 2 |
| C89×#1800 | 2 |
| #8353 | 89 |