Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
520 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26020104 | C2 | semidirect |
| 3. #26018078 | C2 | semidirect |
| 5. C89×#1272 | C2 | semidirect |
| 149. #1272 | D89 | semidirect |
| 151. C89 | #7635 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022795 | 2 |
| #26020104 | 2 |
| #26018078 | 2 |
| #26018072 | 2 |
| C89×#1272 | 2 |
| #7635 | 89 |