Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
522 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 107 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. C8×C22⋊Dic89 | C2 | semidirect |
| 3. #26018773 | C2 | semidirect |
| 5. #26018617 | C2 | semidirect |
| 7. C89×#1810 | C2 | semidirect |
| 8. C22×#13083563 | C4 | semidirect |
| 15. C2×#15667944 | C4 | semidirect |
| 16. C2×#15667937 | C4 | semidirect |
| 17. C2×#15667934 | C4 | semidirect |
| 217. #1810 | D89 | semidirect |
| 223. C89 | #9813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151827 | 2 |
| C8×C22⋊Dic89 | 2 |
| #26018773 | 2 |
| #26018769 | 2 |
| #26018617 | 2 |
| #26018613 | 2 |
| C89×#1810 | 2 |
| #9813 | 89 |