Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 115 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×#16810447 | C2 | semidirect |
| 4. #20275495 | C2 | semidirect |
| 5. #20272828 | C2 | semidirect |
| 6. #20272801 | C2 | semidirect |
| 14. #16810439 | C4 | semidirect |
| 15. #16810436 | C4 | semidirect |
| 169. C53 | #12952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810447 | 2 |
| #20276464 | 2 |
| C2×#16810433 | 2 |
| #20275495 | 2 |
| #20272828 | 2 |
| #20272801 | 2 |
| C53×#2957 | 2 |
| #12952 | 53 |