Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
548 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 548 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. #26018769 | C2 | semidirect |
| 4. #26018613 | C2 | semidirect |
| 5. C89×#1810 | C2 | semidirect |
| 6. C22×D712 | C4 | semidirect |
| 12. C2×#15667946 | C4 | semidirect |
| 13. C2×#15667934 | C4 | semidirect |
| 172. #1810 | D89 | semidirect |
| 176. C89 | #9815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151834 | 2 |
| C8×C22⋊Dic89 | 2 |
| #26018769 | 2 |
| #26018613 | 2 |
| C89×#1810 | 2 |
| #9815 | 89 |