Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
634 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. #26020320 | C2 | semidirect |
| 3. #26018072 | C2 | semidirect |
| 4. C89×#1797 | C2 | semidirect |
| 184. #1797 | D89 | semidirect |
| 186. C89 | #7724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028597 | 2 |
| #26020320 | 2 |
| #26018072 | 2 |
| C89×#1797 | 2 |
| #7724 | 89 |