Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
420 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 127 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. #26019022 | C2 | semidirect |
| 4. #26018149 | C2 | semidirect |
| 139. C89 | #8862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028816 | 2 |
| #26019022 | 2 |
| #26018566 | 2 |
| #26018149 | 2 |
| C89×#1798 | 2 |
| #8862 | 89 |