Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
420 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 82 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. #20290597 | C2 | semidirect |
| 3. #20289804 | C2 | semidirect |
| 14. #16810646 | C4 | semidirect |
| 16. #16810590 | C4 | semidirect |
| 17. C2×#13133127 | C4 | semidirect |
| 18. C2×#131×C53 | C4 | semidirect |
| 141. C2×#131 | #6157 | semidirect |
| 154. C53 | #12808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290986 | 2 |
| #20290597 | 2 |
| #20289804 | 2 |
| #20283431 | 2 |
| #12808 | 53 |