Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #26031202 | C2 | semidirect |
| 4. #26021240 | C2 | semidirect |
| 5. #26018846 | C2 | semidirect |
| 7. C89×#1299 | C2 | semidirect |
| 187. #1299 | D89 | semidirect |
| 188. C89 | #10107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031640 | 2 |
| #26031202 | 2 |
| #26030711 | 2 |
| #26021240 | 2 |
| #26018846 | 2 |
| #26018668 | 2 |
| C89×#1299 | 2 |
| #10107 | 89 |