Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
254 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 125. C89 | #13541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020993 | 2 |
| #26020425 | 2 |
| #26018360 | 2 |
| #26018352 | 2 |
| #26018351 | 2 |
| #26018335 | 2 |
| C89×#1387 | 2 |
| #13541 | 89 |