Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1122 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1122 conjugacy classes of subgroups — too many to draw. Only its 191 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 |
|---|---|---|
| 1. #26028571 | C2 | semidirect |
| 2. #26022734 | C2 | semidirect |
| 3. #26021604 | C2 | semidirect |
| 5. #26020711 | C2 | semidirect |
| 6. #26020533 | C2 | semidirect |
| 7. #26020329 | C2 | semidirect |
| 212. C89 | #24113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028571 | 2 |
| #26022734 | 2 |
| #26021604 | 2 |
| #26021500 | 2 |
| #26020711 | 2 |
| #26020533 | 2 |
| #26020329 | 2 |
| C89×#3491 | 2 |
| #24113 | 89 |