Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
202 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 5. C2×#13133267 | C4 | semidirect |
| 42. C2×C4×C53 | C32 | semidirect |
| 79. C53 | #7465 | semidirect |
| 112. C2×C4 | #13133267 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133267 | 2 |
| C2×C4×#11719908 | 2 |
| #7465 | 53 |