Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
194 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 65 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×#16810463 | C2 | semidirect |
| 4. #20272914 | C2 | semidirect |
| 5. #20272896 | C2 | semidirect |
| 6. #20272895 | C2 | semidirect |
| 79. C22×C53 | Q64 | semidirect |
| 112. C53 | #13695 | semidirect |
| 170. C22 | #16810463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810463 | 2 |
| C22×#13133123 | 2 |
| #20276806 | 2 |
| #20272914 | 2 |
| #20272896 | 2 |
| #20272895 | 2 |
| C53×#2216 | 2 |
| #13695 | 53 |