Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
420 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26020296 | C2 | semidirect |
| 4. #26018372 | C2 | semidirect |
| 6. C2×#15668019 | C4 | semidirect |
| 11. #19151622 | C4 | semidirect |
| 13. #19151565 | C4 | semidirect |
| 15. C2×#15667923 | C4 | semidirect |
| 153. C89 | #12808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028970 | 2 |
| #26021917 | 2 |
| #26020296 | 2 |
| #26018372 | 2 |
| C89×#2126 | 2 |
| #12808 | 89 |