Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
334 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 41 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. #26018184 | C2 | semidirect |
| 3. C89×#1393 | C2 | semidirect |
| 5. C2×#15668009 | C4 | semidirect |
| 7. #19151353 | C4 | semidirect |
| 127. #1393 | D89 | semidirect |
| 129. C89 | #7402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021322 | 2 |
| #26018184 | 2 |
| C89×#1393 | 2 |
| #7402 | 89 |