Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
452 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20283887 | C2 | semidirect |
| 3. #20275548 | C2 | semidirect |
| 4. #20273202 | C2 | semidirect |
| 5. #20272607 | C2 | semidirect |
| 6. #20272606 | C2 | semidirect |
| 7. C53×#1496 | C2 | semidirect |
| 9. #16811029 | C4 | semidirect |
| 10. #16811010 | C4 | semidirect |
| 11. #16810987 | C4 | semidirect |
| 12. #16810985 | C4 | semidirect |
| 214. #1496 | D53 | semidirect |
| 250. C53 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285304 | 2 |
| #20283887 | 2 |
| #20275548 | 2 |
| #20273202 | 2 |
| #20272607 | 2 |
| #20272606 | 2 |
| C53×#1496 | 2 |
| #8997 | 53 |