Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
402 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #26022046 | C2 | semidirect |
| 3. C2×#19151410 | C2 | semidirect |
| 4. C2×#19151410 | C2 | semidirect |
| 5. #26021880 | C2 | semidirect |
| 6. #26018363 | C2 | semidirect |
| 7. C89×#1813 | C2 | semidirect |
| 169. #1813 | D89 | semidirect |
| 171. C89 | #13389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151868 | 2 |
| #26022046 | 2 |
| C2×#19151410 | 2 |
| #26021880 | 2 |
| #26018363 | 2 |
| C89×#1813 | 2 |
| #13389 | 89 |