Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
802 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #26023083 | C2 | semidirect |
| 3. #26021088 | C2 | semidirect |
| 4. #26020197 | C2 | semidirect |
| 5. #26018767 | C2 | semidirect |
| 6. #26018157 | C2 | semidirect |
| 7. C89×#1297 | C2 | semidirect |
| 9. C2×#15668040 | C4 | semidirect |
| 16. #19151600 | C4 | semidirect |
| 35. C22×D356 | C2×C4 | semidirect |
| 51. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 65. C2×M16×C89 | C2×C4 | semidirect |
| 188. D356 | #99 | semidirect |
| 245. #1297 | D89 | semidirect |
| 246. C89 | #9365 | semidirect |
| 285. C2×M16 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029506 | 2 |
| #26023083 | 2 |
| #26021088 | 2 |
| #26020197 | 2 |
| #26018767 | 2 |
| #26018157 | 2 |
| C89×#1297 | 2 |
| #9365 | 89 |