Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
586 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26018272 | C2 | semidirect |
| 4. #26018251 | C2 | semidirect |
| 6. C2×#15667991 | C4 | semidirect |
| 8. #19151523 | C4 | semidirect |
| 10. #19151510 | C4 | semidirect |
| 16. C4×C22⋊Dic89 | C4 | semidirect |
| 23. C22×Dic178 | C2×C4 | semidirect |
| 27. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 42. #15667919 | C2×C4 | semidirect |
| 43. #15667919 | C2×C4 | semidirect |
| 221. C89 | #11759 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025410 | 2 |
| #26018579 | 2 |
| #26018272 | 2 |
| #26018251 | 2 |
| C2×#342×C89 | 2 |
| #11759 | 89 |