Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
456 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. C2×#19151415 | C2 | semidirect |
| 5. #26021167 | C2 | semidirect |
| 6. #26018364 | C2 | semidirect |
| 7. C89×#1378 | C2 | semidirect |
| 12. #19152041 | C4 | semidirect |
| 173. #1378 | D89 | semidirect |
| 174. C89 | #13031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152041 | 2 |
| #26029170 | 2 |
| #26022002 | 2 |
| C2×#19151415 | 2 |
| #26021167 | 2 |
| #26018364 | 2 |
| C89×#1378 | 2 |
| #13031 | 89 |