Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
282 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
|---|---|---|
| 3. #20289634 | C2 | semidirect |
| 16. #13133292 | C8 | semidirect |
| 86. C53 | #11406 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133292 | 2 |
| #20289919 | 2 |
| #20289634 | 2 |
| #346×D53 | 2 |
| #11406 | 53 |