Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
314 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 157. C89 | #11495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151727 | 2 |
| #26022052 | 2 |
| #26022048 | 2 |
| #26018192 | 2 |
| #26018191 | 2 |
| C89×#1322 | 2 |
| #11495 | 89 |