Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
406 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 18. C2×#11719917 | C8 | semidirect |
| 29. C2×M16×C53 | C8 | semidirect |
| 140. C53 | #7034 | semidirect |
| 150. C2×M16 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290569 | 2 |
| #20274408 | 2 |
| #7034 | 53 |