Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
384 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 384 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. C4×#15667944 | C2 | semidirect |
| 4. #26018107 | C2 | semidirect |
| 5. C89×#1568 | C2 | semidirect |
| 7. #19151728 | C4 | semidirect |
| 8. C8×Dic178 | C4 | semidirect |
| 9. #19151677 | C4 | semidirect |
| 11. C8×D356 | C4 | semidirect |
| 155. #1568 | D89 | semidirect |
| 158. C89 | #8696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029227 | 2 |
| C4×#15667944 | 2 |
| #26018778 | 2 |
| #26018107 | 2 |
| C89×#1568 | 2 |
| #8696 | 89 |