Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
454 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26023545 | C2 | semidirect |
| 4. #26018154 | C2 | semidirect |
| 5. C89×#1274 | C2 | semidirect |
| 22. #15668012 | Q8 | semidirect |
| 23. #15668009 | Q8 | semidirect |
| 145. #1274 | D89 | semidirect |
| 146. C89 | #10370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023545 | 2 |
| #26021084 | 2 |
| #26018748 | 2 |
| #26018154 | 2 |
| C89×#1274 | 2 |
| #10370 | 89 |