Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
384 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 180. C89 | #8774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023212 | 2 |
| C4×#15667930 | 2 |
| #26018595 | 2 |
| #26018146 | 2 |
| #26018144 | 2 |
| #26018116 | 2 |
| C89×#1288 | 2 |
| #8774 | 89 |