Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
294 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 16. #19151350 | C4 | semidirect |
| 18. #19151348 | C4 | semidirect |
| 131. C89 | #9632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020389 | 2 |
| #26020122 | 2 |
| #26019022 | 2 |
| #26018998 | 2 |
| #26018154 | 2 |
| #26018153 | 2 |
| C89×#1571 | 2 |
| #9632 | 89 |