Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
358 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 96 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. #20291062 | C2 | semidirect |
| 2. C2×#16811548 | C2 | semidirect |
| 5. #20289793 | C2 | semidirect |
| 6. #20289787 | C2 | semidirect |
| 22. #16811041 | C4 | semidirect |
| 23. #16811040 | C4 | semidirect |
| 25. #16811039 | C4 | semidirect |
| 30. C53×#504 | C4 | semidirect |
| 192. #504 | #6157 | semidirect |
| 209. C53 | #12833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291062 | 2 |
| C2×#16811548 | 2 |
| #20290603 | 2 |
| #20290601 | 2 |
| #20289793 | 2 |
| #20289787 | 2 |
| #20287816 | 2 |
| #12833 | 53 |