Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
328 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#16810443 | C2 | semidirect |
| 5. #20272796 | C2 | semidirect |
| 6. #20272795 | C2 | semidirect |
| 7. C2×C53×#347 | C2 | semidirect |
| 147. C2×#347 | D53 | semidirect |
| 172. C53 | #13128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810443 | 2 |
| C2×#16810404 | 2 |
| #20274500 | 2 |
| #20272796 | 2 |
| #20272795 | 2 |
| C2×C53×#347 | 2 |
| #13128 | 53 |