Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
306 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 27. #97×C89 | C8 | semidirect |
| 92. C89 | #8801 | semidirect |
| 114. #97 | #10623494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018097 | 2 |
| #26018085 | 2 |
| #26018083 | 2 |
| C4×#97×C89 | 2 |
| #8801 | 89 |