Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
204 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 119. C53 | #12079 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276584 | 2 |
| #20273535 | 2 |
| #20272780 | 2 |
| #20272685 | 2 |
| #20272684 | 2 |
| #20272636 | 2 |
| C53×#1593 | 2 |
| #12079 | 53 |