Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
454 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 150. C89 | #9779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151977 | 2 |
| #26020389 | 2 |
| #26018925 | 2 |
| #26018924 | 2 |
| #26018923 | 2 |
| #26018545 | 2 |
| C89×#1546 | 2 |
| #9779 | 89 |