Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
194 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26022137 | C2 | semidirect |
| 3. #26022127 | C2 | semidirect |
| 4. #26018441 | C2 | semidirect |
| 5. #26018438 | C2 | semidirect |
| 6. #26018387 | C2 | semidirect |
| 7. C89×#1426 | C2 | semidirect |
| 12. #19151437 | C4 | semidirect |
| 13. D2848 | C4 | semidirect |
| 25. Dic712 | C2×C4 | semidirect |
| 29. D1424 | C2×C4 | semidirect |
| 38. C32×C89 | C2×C4 | semidirect |
| 91. #1426 | D89 | semidirect |
| 95. C89 | #13658 | semidirect |
| 126. C32 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022567 | 2 |
| #26022137 | 2 |
| #26022127 | 2 |
| #26018441 | 2 |
| #26018438 | 2 |
| #26018387 | 2 |
| C89×#1426 | 2 |
| #13658 | 89 |