Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
530 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20275633 | C2 | semidirect |
| 3. #20273313 | C2 | semidirect |
| 4. #20273261 | C2 | semidirect |
| 5. #20272579 | C2 | semidirect |
| 6. #20272571 | C2 | semidirect |
| 7. C53×#2337 | C2 | semidirect |
| 9. #16811013 | C4 | semidirect |
| 10. #16810982 | C4 | semidirect |
| 35. #13133217 | C2×C4 | semidirect |
| 36. #13133214 | C2×C4 | semidirect |
| 52. #13133128 | C2×C4 | semidirect |
| 216. #2337 | D53 | semidirect |
| 252. C53 | #9381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285702 | 2 |
| #20275633 | 2 |
| #20273313 | 2 |
| #20273261 | 2 |
| #20272579 | 2 |
| #20272571 | 2 |
| C53×#2337 | 2 |
| #9381 | 53 |