Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
680 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 680 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 |
|---|---|---|
| 3. #20272735 | C2 | semidirect |
| 5. C23×Dic106 | C4 | semidirect |
| 10. #16810535 | C4 | semidirect |
| 13. C2×#13133124 | C4 | semidirect |
| 211. C53 | #11808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810535 | 2 |
| #20273042 | 2 |
| #20272735 | 2 |
| C53×#1819 | 2 |
| #11808 | 53 |