Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
508 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 246. C89 | #13425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26027087 | 2 |
| C2×#19151387 | 2 |
| #26020663 | 2 |
| #26020641 | 2 |
| #26020535 | 2 |
| #26018369 | 2 |
| C2×#354×C89 | 2 |
| #13425 | 89 |