Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
272 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 131. C89 | #13491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151415 | 2 |
| #26021973 | 2 |
| #26021167 | 2 |
| #26020376 | 2 |
| #26018367 | 2 |
| #26018364 | 2 |
| C89×#1378 | 2 |
| #13491 | 89 |