Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
216 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 123. C53 | #13545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275496 | 2 |
| #20274838 | 2 |
| #20272828 | 2 |
| #20272820 | 2 |
| #20272814 | 2 |
| #20272802 | 2 |
| C53×#1389 | 2 |
| #13545 | 53 |