Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
602 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 178. C53 | #11288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291357 | 2 |
| C2×#16811504 | 2 |
| #20290381 | 2 |
| #20274446 | 2 |
| #11288 | 53 |