Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
310 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 174. C53 | #12292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286056 | 2 |
| #20276917 | 2 |
| #20276209 | 2 |
| #20272728 | 2 |
| #20272727 | 2 |
| #20272654 | 2 |
| C53×#2236 | 2 |
| #12292 | 53 |