Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
672 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 672 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 |
|---|---|---|
| 3. #26021927 | C2 | semidirect |
| 5. #26018382 | C2 | semidirect |
| 6. #26018372 | C2 | semidirect |
| 7. C89×#2123 | C2 | semidirect |
| 9. C2×#15668043 | C4 | semidirect |
| 10. C22×#13083561 | C4 | semidirect |
| 18. #19151602 | C4 | semidirect |
| 19. #19151592 | C4 | semidirect |
| 49. C2×#13083558 | C2×C4 | semidirect |
| 50. C22×#10623494 | C2×C4 | semidirect |
| 70. C22×Q8×C89 | C2×C4 | semidirect |
| 79. #117×C89 | C2×C4 | semidirect |
| 255. #2123 | D89 | semidirect |
| 259. C89 | #13100 | semidirect |
| 290. C22×Q8 | C4×D89 | semidirect |
| 317. #117 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029527 | 2 |
| #26028711 | 2 |
| #26021927 | 2 |
| #26020223 | 2 |
| #26018382 | 2 |
| #26018372 | 2 |
| C89×#2123 | 2 |
| #13100 | 89 |