Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
522 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 2. #20289543 | C2 | semidirect |
| 3. #20289539 | C2 | semidirect |
| 38. #117×C53 | C8 | semidirect |
| 153. C53 | #8731 | semidirect |
| 159. #117 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289946 | 2 |
| #20289543 | 2 |
| #20289539 | 2 |
| #117×Dic53 | 2 |
| #8731 | 53 |