Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
902 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 902 conjugacy classes of subgroups — too many to draw. Only its 139 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. C2×#19151334 | C2 | semidirect |
| 4. #26018131 | C2 | semidirect |
| 6. C2×#15667991 | C4 | semidirect |
| 12. #19151458 | C4 | semidirect |
| 192. C89 | #9154 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028539 | 2 |
| #26020162 | 2 |
| C2×#19151334 | 2 |
| #26018131 | 2 |
| C2×#381×C89 | 2 |
| #9154 | 89 |