Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
334 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 13. #16810441 | C4 | semidirect |
| 115. C53 | #12657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276470 | 2 |
| C2×#16810401 | 2 |
| #20274403 | 2 |
| #20272794 | 2 |
| C2×C53×#347 | 2 |
| #12657 | 53 |