Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
248 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #26018174 | C2 | semidirect |
| 5. #26018174 | C2 | semidirect |
| 6. #26018173 | C2 | semidirect |
| 7. C89×#1313 | C2 | semidirect |
| 57. #13083549 | M16 | semidirect |
| 106. #1313 | D89 | semidirect |
| 107. C89 | #11414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022053 | 2 |
| #26021845 | 2 |
| #26018538 | 2 |
| #26018174 | 2 |
| #26018173 | 2 |
| C89×#1313 | 2 |
| #11414 | 89 |