Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
770 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 1. #26028695 | C2 | semidirect |
| 3. #26020169 | C2 | semidirect |
| 4. #26018781 | C2 | semidirect |
| 5. #26018106 | C2 | semidirect |
| 6. #26018104 | C2 | semidirect |
| 7. C89×#1510 | C2 | semidirect |
| 10. C2×#15668008 | C4 | semidirect |
| 11. C2×#15667999 | C4 | semidirect |
| 20. #19151503 | C4 | semidirect |
| 21. #19151499 | C4 | semidirect |
| 63. C22⋊#10623494 | D4 | semidirect |
| 82. C22⋊C8×C89 | D4 | semidirect |
| 306. #1510 | D89 | semidirect |
| 309. C89 | #9445 | semidirect |
| 379. C22⋊C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028695 | 2 |
| #26023872 | 2 |
| #26020169 | 2 |
| #26018781 | 2 |
| #26018106 | 2 |
| #26018104 | 2 |
| C89×#1510 | 2 |
| #9445 | 89 |