Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
422 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 12. #16810729 | C4 | semidirect |
| 17. #16810440 | C4 | semidirect |
| 18. #16810426 | C4 | semidirect |
| 160. C53 | #12648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810729 | 2 |
| C2×#16810440 | 2 |
| #20276434 | 2 |
| C2×#16810400 | 2 |
| #20274601 | 2 |
| #20272813 | 2 |
| C53×#1386 | 2 |
| #12648 | 53 |