Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1180 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1180 conjugacy classes of subgroups — too many to draw. Only its 203 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×#19151933 | C2 | semidirect |
| 3. #26019276 | C2 | direct (N × H) |
| 4. C2×#19151334 | C2 | semidirect |
| 16. #19151933 | C22 | semidirect |
| 20. #19151334 | C22 | semidirect |
| 210. C2×C89 | #1614 | semidirect |
| 220. C89 | C2×#1614 | semidirect |
| 423. C2 | #26019276 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152224 | 2 |
| C2×#19151933 | 2 |
| #26019276 | 2 |
| C2×#19151334 | 2 |
| C2×#19151322 | 2 |
| C2×#399×C89 | 2 |
| C2×#1614 | 89 |