Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
494 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20273279 | C2 | semidirect |
| 5. #20272618 | C2 | semidirect |
| 6. #20272574 | C2 | semidirect |
| 7. C53×#1503 | C2 | semidirect |
| 10. #16810910 | C4 | semidirect |
| 11. #16810900 | C4 | semidirect |
| 188. #1503 | D53 | semidirect |
| 219. C53 | #9177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284508 | 2 |
| #20277686 | 2 |
| #20273279 | 2 |
| #20273105 | 2 |
| #20272618 | 2 |
| #20272574 | 2 |
| C53×#1503 | 2 |
| #9177 | 53 |