Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
420 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 3. #20272821 | C2 | semidirect |
| 8. #16810661 | C4 | semidirect |
| 10. C2×#13133151 | C4 | semidirect |
| 11. C2×#13133151 | C4 | semidirect |
| 157. C53 | #12870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810661 | 2 |
| #20274740 | 2 |
| #20272821 | 2 |
| C53×#2112 | 2 |
| #12870 | 53 |