Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
262 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 7. C4⋊#11719910 | C4 | semidirect |
| 9. #16811511 | C4 | semidirect |
| 119. C53 | #7170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11719910 | 2 |
| C2×#16811511 | 2 |
| #20274584 | 2 |
| #7170 | 53 |