Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
908 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 407 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. #26020008 | C2 | semidirect |
| 8. #19151553 | C4 | semidirect |
| 9. M16×Dic89 | C4 | semidirect |
| 23. #15667922 | C2×C4 | semidirect |
| 24. C8×Dic89 | C2×C4 | semidirect |
| 90. C89 | #20370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028670 | 2 |
| #26020008 | 2 |
| C2×#19151355 | 2 |
| C2×#338×C89 | 2 |
| #20370 | 89 |