Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
636 conjugacy classes of subgroups; only the 391 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 391 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. #26022025 | C2 | semidirect |
| 4. C2×#19151421 | C2 | semidirect |
| 16. #504×C89 | C4 | semidirect |
| 35. M32×C89 | C2×C4 | semidirect |
| 37. C2×C16×C89 | C2×C4 | semidirect |
| 89. C89 | #33404 | semidirect |
| 93. #504 | Dic89 | semidirect |
| 113. M32 | C2×Dic89 | semidirect |
| 115. C2×C16 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028863 | 2 |
| #26028847 | 2 |
| #26022025 | 2 |
| C2×#19151421 | 2 |
| C89×#3407 | 2 |
| #33404 | 89 |