Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. #26020055 | C2 | semidirect |
| 4. #26018373 | C2 | semidirect |
| 5. C89×#1392 | C2 | semidirect |
| 7. C22×C8×D89 | C4 | semidirect |
| 11. #19151624 | C4 | semidirect |
| 13. #19151561 | C4 | semidirect |
| 15. #19151556 | C4 | semidirect |
| 16. #19151389 | C4 | semidirect |
| 17. #19151386 | C4 | semidirect |
| 152. #1392 | D89 | semidirect |
| 154. C89 | #12623 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028949 | 2 |
| #26021894 | 2 |
| #26020055 | 2 |
| #26018373 | 2 |
| C89×#1392 | 2 |
| #12623 | 89 |