Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1128 conjugacy classes of subgroups; only the 391 normal subgroups are shown.
This group has 1128 conjugacy classes of subgroups — too many to draw. Only its 391 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 |
|---|---|---|
| 1. #26033355 | C2 | semidirect |
| 2. #26028847 | C2 | semidirect |
| 3. #26021988 | C2 | semidirect |
| 4. C2×#19151408 | C2 | semidirect |
| 8. C2×#15667952 | C22 | semidirect |
| 10. #19151636 | C22 | semidirect |
| 11. C2×#15667944 | C22 | semidirect |
| 12. #19151408 | C22 | semidirect |
| 13. #19151408 | C22 | semidirect |
| 15. #578×C89 | C4 | semidirect |
| 17. #576×C89 | C4 | semidirect |
| 43. #135×C89 | C2×C4 | semidirect |
| 45. C2×Q16×C89 | C2×C4 | semidirect |
| 47. C2×D8×C89 | C2×C4 | semidirect |
| 131. C89 | #33388 | semidirect |
| 133. #578 | Dic89 | semidirect |
| 135. #576 | Dic89 | semidirect |
| 158. #135 | C2×Dic89 | semidirect |
| 160. C2×Q16 | C2×Dic89 | semidirect |
| 162. C2×D8 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033355 | 2 |
| #26028847 | 2 |
| #26021988 | 2 |
| C2×#19151408 | 2 |
| C89×#3584 | 2 |
| #33388 | 89 |