Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
232 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 3. #26018317 | C2 | semidirect |
| 35. #13083549 | M16 | semidirect |
| 88. C89 | #12020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667952 | 2 |
| #26019008 | 2 |
| #26018317 | 2 |
| C89×#1566 | 2 |
| #12020 | 89 |