Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 13. #19151626 | C4 | semidirect |
| 14. #19151624 | C4 | semidirect |
| 18. M16×Dic89 | C4 | semidirect |
| 19. C2×C8×Dic89 | C4 | semidirect |
| 174. C89 | #12864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028892 | 2 |
| #26020357 | 2 |
| #26020353 | 2 |
| #26018381 | 2 |
| #26018374 | 2 |
| #26018372 | 2 |
| C89×#1395 | 2 |
| #12864 | 89 |