Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
426 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26020001 | C2 | semidirect |
| 3. #26018074 | C2 | semidirect |
| 5. C89×#1831 | C2 | semidirect |
| 169. #1831 | D89 | semidirect |
| 173. C89 | #7706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028619 | 2 |
| #26020001 | 2 |
| #26018074 | 2 |
| #26018072 | 2 |
| C89×#1831 | 2 |
| #7706 | 89 |