Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
336 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 17. #330×C89 | C4 | semidirect |
| 18. #330×C89 | C4 | semidirect |
| 19. #330×C89 | C4 | semidirect |
| 104. C89 | #8919 | semidirect |
| 116. #330 | Dic89 | semidirect |
| 117. #330 | Dic89 | semidirect |
| 118. #330 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029358 | 2 |
| #26021234 | 2 |
| #26019019 | 2 |
| #26018146 | 2 |
| C89×#1526 | 2 |
| #8919 | 89 |