Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
658 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16810956 | C2 | semidirect |
| 3. C2×#16810360 | C2 | semidirect |
| 5. #20272984 | C2 | semidirect |
| 6. #20272558 | C2 | semidirect |
| 258. C53 | #9969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810956 | 2 |
| C2×#16810939 | 2 |
| C2×#16810360 | 2 |
| C2×#16810357 | 2 |
| #20272984 | 2 |
| #20272558 | 2 |
| C53×#2639 | 2 |
| #9969 | 53 |