Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
470 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26028910 | C2 | semidirect |
| 5. #26018158 | C2 | semidirect |
| 6. #26018140 | C2 | semidirect |
| 7. C89×#1825 | C2 | semidirect |
| 16. #19151641 | C4 | semidirect |
| 17. #19151641 | C4 | semidirect |
| 19. #19151602 | C4 | semidirect |
| 20. #19151602 | C4 | semidirect |
| 225. #1825 | D89 | semidirect |
| 230. C89 | #9348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030192 | 2 |
| #26028910 | 2 |
| #26018819 | 2 |
| #26018611 | 2 |
| #26018158 | 2 |
| #26018140 | 2 |
| C89×#1825 | 2 |
| #9348 | 89 |