Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
248 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 127. C89 | #10689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020973 | 2 |
| #26020392 | 2 |
| #26018154 | 2 |
| #26018153 | 2 |
| #26018149 | 2 |
| #26018082 | 2 |
| C89×#1301 | 2 |
| #10689 | 89 |