Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
540 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 7. C22×C4×Dic89 | C4 | semidirect |
| 12. #19151470 | C4 | semidirect |
| 13. #19151459 | C4 | semidirect |
| 17. C4×C22⋊Dic89 | C4 | semidirect |
| 75. C22×Dic89 | C4⋊C4 | semidirect |
| 87. C22⋊Dic89 | C4⋊C4 | semidirect |
| 198. C4×C89 | #352 | semidirect |
| 219. C89 | #12794 | semidirect |
| 417. C4 | #19151389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667993 | 2 |
| C2×#19151389 | 2 |
| #26020240 | 2 |
| #26018371 | 2 |
| C89×#1800 | 2 |
| #12794 | 89 |