Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
468 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20276387 | C2 | semidirect |
| 3. #20276386 | C2 | semidirect |
| 4. #20276366 | C2 | semidirect |
| 5. #20274759 | C2 | semidirect |
| 6. #20274518 | C2 | semidirect |
| 7. C53×#2122 | C2 | semidirect |
| 8. C22×#11719922 | C4 | semidirect |
| 16. #16810659 | C4 | semidirect |
| 17. #16810628 | C4 | semidirect |
| 18. #16810627 | C4 | semidirect |
| 217. #2122 | D53 | semidirect |
| 250. C53 | #13231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284360 | 2 |
| #20276387 | 2 |
| #20276386 | 2 |
| #20276366 | 2 |
| #20274759 | 2 |
| #20274518 | 2 |
| C53×#2122 | 2 |
| #13231 | 53 |