Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
324 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 67 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×#19151437 | C2 | semidirect |
| 3. #26022343 | C2 | semidirect |
| 4. #26018431 | C2 | semidirect |
| 5. C89×C22⋊C32 | C2 | semidirect |
| 7. C2×Dic712 | C22 | semidirect |
| 13. #19151424 | C22 | semidirect |
| 16. C2×C32×C89 | C22 | semidirect |
| 77. C22×C89 | SD64 | semidirect |
| 98. C22⋊C32 | D89 | semidirect |
| 99. C89 | #13664 | semidirect |
| 108. C2×C32 | C2×D89 | semidirect |
| 175. C22 | #19151437 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1424 | 2 |
| C2×#19151437 | 2 |
| #26022343 | 2 |
| #26018431 | 2 |
| C89×C22⋊C32 | 2 |
| #13664 | 89 |