Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
494 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 494 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 |
|---|---|---|
| 3. #26018816 | C2 | semidirect |
| 5. #26018155 | C2 | semidirect |
| 6. #26018111 | C2 | semidirect |
| 7. C89×#1503 | C2 | semidirect |
| 10. #19151885 | C4 | semidirect |
| 11. #19151875 | C4 | semidirect |
| 194. #1503 | D89 | semidirect |
| 198. C89 | #9177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030045 | 2 |
| #26023223 | 2 |
| #26018816 | 2 |
| #26018642 | 2 |
| #26018155 | 2 |
| #26018111 | 2 |
| C89×#1503 | 2 |
| #9177 | 89 |