Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
940 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 940 conjugacy classes of subgroups — too many to draw. Only its 187 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. #26019296 | C2 | semidirect |
| 5. #26019228 | C2 | semidirect |
| 120. C22×C4×C89 | Q16 | semidirect |
| 206. C89 | #18295 | semidirect |
| 300. C22×C4 | Dic356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152229 | 2 |
| #26031027 | 2 |
| #26026065 | 2 |
| #26019296 | 2 |
| #26019228 | 2 |
| #26018825 | 2 |
| C2×#324×C89 | 2 |
| #18295 | 89 |