Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
568 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #26018283 | C2 | semidirect |
| 5. #26018282 | C2 | semidirect |
| 6. #26018281 | C2 | semidirect |
| 7. C89×#1354 | C2 | semidirect |
| 214. #1354 | D89 | semidirect |
| 215. C89 | #11904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023612 | 2 |
| #26020243 | 2 |
| #26018569 | 2 |
| #26018283 | 2 |
| #26018282 | 2 |
| #26018281 | 2 |
| C89×#1354 | 2 |
| #11904 | 89 |