Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
318 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 146. C89 | #13479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022038 | 2 |
| C2×#19151418 | 2 |
| C2×#19151413 | 2 |
| #26021973 | 2 |
| #26021111 | 2 |
| #26020998 | 2 |
| C89×#1387 | 2 |
| #13479 | 89 |