Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
214 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 35. #13133163 | C8 | semidirect |
| 119. C53 | #12066 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290310 | 2 |
| #20290308 | 2 |
| #20289741 | 2 |
| #20289676 | 2 |
| #20289675 | 2 |
| #20289632 | 2 |
| #20276583 | 2 |
| #12066 | 53 |