Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
460 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26019226 | C2 | semidirect |
| 4. #26018283 | C2 | semidirect |
| 5. #26018282 | C2 | semidirect |
| 7. C89×#1605 | C2 | semidirect |
| 70. C2×D356 | Q16 | semidirect |
| 192. #1605 | D89 | semidirect |
| 196. C89 | #12220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026626 | 2 |
| #26021405 | 2 |
| #26019226 | 2 |
| #26018283 | 2 |
| #26018282 | 2 |
| #26018183 | 2 |
| C89×#1605 | 2 |
| #12220 | 89 |