Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
234 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 128. C53 | #12885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291058 | 2 |
| #20291050 | 2 |
| #20289770 | 2 |
| #20289769 | 2 |
| #20289766 | 2 |
| #20289765 | 2 |
| #20274469 | 2 |
| #12885 | 53 |