Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
318 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 14. #16811550 | C4 | semidirect |
| 15. #16811549 | C4 | semidirect |
| 16. #16811548 | C4 | semidirect |
| 17. #16811547 | C4 | semidirect |
| 23. #16810401 | C4 | semidirect |
| 24. #16810400 | C4 | semidirect |
| 25. #16810400 | C4 | semidirect |
| 26. C53×#347 | C4 | semidirect |
| 91. C16×C53 | C42 | semidirect |
| 93. #11719908 | C42 | semidirect |
| 165. #347 | #6157 | semidirect |
| 168. C53 | #12677 | semidirect |
| 235. C16 | C4×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291067 | 2 |
| D53⋊#365 | 2 |
| #20290529 | 2 |
| #20290521 | 2 |
| #20289790 | 2 |
| #20289787 | 2 |
| #347×D53 | 2 |
| #12677 | 53 |