Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
494 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26021071 | C2 | semidirect |
| 4. #26018925 | C2 | semidirect |
| 6. #26018082 | C2 | semidirect |
| 7. C89×#1286 | C2 | semidirect |
| 11. #19152003 | C4 | semidirect |
| 12. #19151945 | C4 | semidirect |
| 187. #1286 | D89 | semidirect |
| 189. C89 | #9291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031375 | 2 |
| #26028969 | 2 |
| #26021071 | 2 |
| #26018925 | 2 |
| #26018811 | 2 |
| #26018082 | 2 |
| C89×#1286 | 2 |
| #9291 | 89 |