Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1422 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 1422 conjugacy classes of subgroups — too many to draw. Only its 451 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 |
|---|---|---|
| 12. #383×C89 | C4 | semidirect |
| 43. C42×C89 | C4⋊C4 | semidirect |
| 80. C89 | #14710 | semidirect |
| 85. #383 | Dic89 | semidirect |
| 119. C42 | C4⋊Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151466 | 2 |
| C2×C42×Dic89 | 2 |
| #26018486 | 2 |
| C2×#383×C89 | 2 |
| #14710 | 89 |