Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
320 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 142. C53 | #10663 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275654 | 2 |
| #20274889 | 2 |
| #20273485 | 2 |
| #20273145 | 2 |
| #20273143 | 2 |
| #20272545 | 2 |
| C53×#1570 | 2 |
| #10663 | 53 |