Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
258 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 37 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. #26018373 | C2 | semidirect |
| 3. C89×#1321 | C2 | semidirect |
| 5. C22×D712 | C4 | semidirect |
| 8. #19151363 | C4 | semidirect |
| 103. #1321 | D89 | semidirect |
| 104. C89 | #7398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021361 | 2 |
| #26018373 | 2 |
| C89×#1321 | 2 |
| #7398 | 89 |