Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
452 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #20274518 | C2 | semidirect |
| 5. #20274517 | C2 | semidirect |
| 6. #20272844 | C2 | semidirect |
| 7. C53×#1395 | C2 | semidirect |
| 8. C2×#13133225 | C4 | semidirect |
| 15. #16810646 | C4 | semidirect |
| 18. #16810589 | C4 | semidirect |
| 21. C2×#13133127 | C4 | semidirect |
| 22. #16810421 | C4 | semidirect |
| 23. #16810419 | C4 | semidirect |
| 206. #1395 | D53 | semidirect |
| 236. C53 | #12634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283430 | 2 |
| #20276398 | 2 |
| #20276378 | 2 |
| #20274518 | 2 |
| #20274517 | 2 |
| #20272844 | 2 |
| C53×#1395 | 2 |
| #12634 | 53 |