Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
908 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 407 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 |
|---|---|---|
| 2. #20274471 | C2 | semidirect |
| 8. #16810578 | C4 | semidirect |
| 9. M16×Dic53 | C4 | semidirect |
| 23. #13133127 | C2×C4 | semidirect |
| 24. C8×Dic53 | C2×C4 | semidirect |
| 98. C53 | #20370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283133 | 2 |
| #20274471 | 2 |
| C2×#16810380 | 2 |
| C2×C53×#338 | 2 |
| #20370 | 53 |