Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
430 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 155 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. #26022051 | C2 | semidirect |
| 2. #26018176 | C2 | semidirect |
| 36. C2×D4×C89 | C16 | semidirect |
| 109. C89 | #11487 | semidirect |
| 141. C2×D4 | #13083549 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022051 | 2 |
| #26018176 | 2 |
| C2×C8×D4×C89 | 2 |
| #11487 | 89 |