Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
524 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26030798 | C2 | semidirect |
| 4. #26021199 | C2 | semidirect |
| 6. #26018752 | C2 | semidirect |
| 7. C89×#1283 | C2 | semidirect |
| 116. M16×C89 | SD16 | semidirect |
| 195. #1283 | D89 | semidirect |
| 196. C89 | #10197 | semidirect |
| 286. M16 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031569 | 2 |
| #26031179 | 2 |
| #26030798 | 2 |
| #26021199 | 2 |
| #26021171 | 2 |
| #26018752 | 2 |
| C89×#1283 | 2 |
| #10197 | 89 |