Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
658 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 1. C2×#19151929 | C2 | semidirect |
| 4. C2×#19151336 | C2 | semidirect |
| 6. #26018519 | C2 | semidirect |
| 7. C89×#1280 | C2 | semidirect |
| 234. #1280 | D89 | semidirect |
| 235. C89 | #9971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151929 | 2 |
| C2×#19151912 | 2 |
| #26026180 | 2 |
| C2×#19151336 | 2 |
| C2×#19151333 | 2 |
| #26018519 | 2 |
| C89×#1280 | 2 |
| #9971 | 89 |