Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
420 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 178. C89 | #10127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031462 | 2 |
| #26031458 | 2 |
| #26018725 | 2 |
| #26018674 | 2 |
| #26018608 | 2 |
| #26018124 | 2 |
| C89×#3166 | 2 |
| #10127 | 89 |