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. #26023080 | C2 | semidirect |
| 3. #26020197 | C2 | semidirect |
| 4. #26018768 | C2 | semidirect |
| 5. #26018158 | C2 | semidirect |
| 6. #26018138 | C2 | semidirect |
| 7. C89×#1964 | C2 | semidirect |
| 9. C2×#15668038 | C4 | semidirect |
| 15. #19151597 | C4 | semidirect |
| 43. C2×#13083558 | C2×C4 | semidirect |
| 60. C22×D4×C89 | C2×C4 | semidirect |
| 67. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 188. D356 | #99 | semidirect |
| 241. #1964 | D89 | semidirect |
| 246. C89 | #9365 | semidirect |
| 277. C22×D4 | C4×D89 | semidirect |
| 292. C2×C4⋊C4 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029502 | 2 |
| #26023080 | 2 |
| #26020197 | 2 |
| #26018768 | 2 |
| #26018158 | 2 |
| #26018138 | 2 |
| C89×#1964 | 2 |
| #9365 | 89 |