Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
672 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#19151536 | C2 | semidirect |
| 5. C2×#19151323 | C2 | semidirect |
| 6. #26018130 | C2 | semidirect |
| 7. C89×#1824 | C2 | semidirect |
| 243. #1824 | D89 | semidirect |
| 247. C89 | #9921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151916 | 2 |
| #26025997 | 2 |
| C2×#19151536 | 2 |
| C2×#19151333 | 2 |
| C2×#19151323 | 2 |
| #26018130 | 2 |
| C89×#1824 | 2 |
| #9921 | 89 |