Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
532 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 532 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 |
|---|---|---|
| 3. #26020432 | C2 | semidirect |
| 4. #26018100 | C2 | semidirect |
| 94. C22⋊C4×C89 | M16 | semidirect |
| 182. C89 | #8852 | semidirect |
| 271. C22⋊C4 | #13083558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029281 | 2 |
| #26020545 | 2 |
| #26020432 | 2 |
| #26018100 | 2 |
| C4×#99×C89 | 2 |
| #8852 | 89 |