Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
514 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 159 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. C2×#19151401 | C2 | semidirect |
| 4. C2×C4×#13083549 | C2 | semidirect |
| 5. C89×#1846 | C2 | semidirect |
| 12. #19151982 | C4 | semidirect |
| 138. #1846 | D89 | semidirect |
| 139. C89 | #13204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151982 | 2 |
| C2×#19151401 | 2 |
| C2×#19151398 | 2 |
| C2×C4×#13083549 | 2 |
| C89×#1846 | 2 |
| #13204 | 89 |