Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
316 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26022504 | C2 | semidirect |
| 4. #26019868 | C2 | semidirect |
| 6. #26018168 | C2 | semidirect |
| 7. C89×#2247 | C2 | semidirect |
| 99. #2247 | D89 | semidirect |
| 103. C89 | #12520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022509 | 2 |
| #26022508 | 2 |
| #26022504 | 2 |
| #26019868 | 2 |
| #26019859 | 2 |
| #26018168 | 2 |
| C89×#2247 | 2 |
| #12520 | 89 |