Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
412 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 237. C53 | #9270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291512 | 2 |
| #20290908 | 2 |
| #20290233 | 2 |
| C2×#16811482 | 2 |
| #20289606 | 2 |
| #20289559 | 2 |
| #20285864 | 2 |
| #9270 | 53 |