Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
950 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 207 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. #26021654 | C2 | semidirect |
| 4. #26021653 | C2 | semidirect |
| 5. #26021652 | C2 | semidirect |
| 7. C89×#2070 | C2 | semidirect |
| 145. D89 | #2070 | direct (N × H) |
| 151. #2070 | D89 | direct (N × H) |
| 153. C89 | C2×#2070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #430×D89 | 2 |
| C2×#101×D89 | 2 |
| #26021654 | 2 |
| #26021653 | 2 |
| #26021652 | 2 |
| #338×D89 | 2 |
| C89×#2070 | 2 |
| C2×#2070 | 89 |