Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
388 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 20. #16810439 | C4 | semidirect |
| 176. C53 | #12941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283583 | 2 |
| #20276501 | 2 |
| C2×#16810439 | 2 |
| #20275498 | 2 |
| #20272811 | 2 |
| #20272803 | 2 |
| C2×C53×#358 | 2 |
| #12941 | 53 |