Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
820 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 171 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. #26031479 | C2 | semidirect |
| 2. #26030634 | C2 | semidirect |
| 3. #26019586 | C2 | semidirect |
| 4. #26019580 | C2 | semidirect |
| 5. #26019575 | C2 | semidirect |
| 6. #26018890 | C2 | semidirect |
| 7. #26018859 | C2 | semidirect |
| 210. C89 | #19005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031479 | 2 |
| #26030634 | 2 |
| #26019586 | 2 |
| #26019580 | 2 |
| #26019575 | 2 |
| #26018890 | 2 |
| #26018859 | 2 |
| C89×#3531 | 2 |
| #19005 | 89 |