Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
640 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 640 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. #26028733 | C2 | semidirect |
| 3. #26021943 | C2 | semidirect |
| 4. #26021903 | C2 | semidirect |
| 5. #26020228 | C2 | semidirect |
| 6. #26018381 | C2 | semidirect |
| 7. C89×#1392 | C2 | semidirect |
| 9. C2×#15668040 | C4 | semidirect |
| 10. C22×#13083563 | C4 | semidirect |
| 19. #19151608 | C4 | semidirect |
| 20. #19151595 | C4 | semidirect |
| 252. #1392 | D89 | semidirect |
| 253. C89 | #13098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029540 | 2 |
| #26028733 | 2 |
| #26021943 | 2 |
| #26021903 | 2 |
| #26020228 | 2 |
| #26018381 | 2 |
| C89×#1392 | 2 |
| #13098 | 89 |