Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
576 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26023406 | C2 | semidirect |
| 3. #26021087 | C2 | semidirect |
| 4. #26018782 | C2 | semidirect |
| 5. #26018769 | C2 | semidirect |
| 6. #26018106 | C2 | semidirect |
| 7. C89×#1305 | C2 | semidirect |
| 11. #19151917 | C4 | semidirect |
| 14. #19151734 | C4 | semidirect |
| 31. C22×D356 | C2×C4 | semidirect |
| 45. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 77. C22⋊C8×C89 | C2×C4 | semidirect |
| 254. #1305 | D89 | semidirect |
| 256. C89 | #9343 | semidirect |
| 320. C22⋊C8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031052 | 2 |
| #26023406 | 2 |
| #26021087 | 2 |
| #26018782 | 2 |
| #26018769 | 2 |
| #26018106 | 2 |
| C89×#1305 | 2 |
| #9343 | 89 |