Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
312 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26022046 | C2 | semidirect |
| 4. #26018332 | C2 | semidirect |
| 5. C89×#1849 | C2 | semidirect |
| 113. #1849 | D89 | semidirect |
| 115. C89 | #13532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022046 | 2 |
| #26021979 | 2 |
| #26021145 | 2 |
| #26018332 | 2 |
| C89×#1849 | 2 |
| #13532 | 89 |