Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
422 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 1. #26031076 | C2 | semidirect |
| 2. #26022203 | C2 | semidirect |
| 3. #26018239 | C2 | semidirect |
| 4. #26018188 | C2 | semidirect |
| 21. C2×Dic356 | D4 | semidirect |
| 33. #15667944 | D4 | semidirect |
| 158. C89 | #12115 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031076 | 2 |
| #26022203 | 2 |
| #26018239 | 2 |
| #26018188 | 2 |
| C89×#2010 | 2 |
| #12115 | 89 |