Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
620 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 10. #16811352 | C4 | semidirect |
| 12. #16811351 | C4 | semidirect |
| 228. C53 | #8495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289210 | 2 |
| #20275695 | 2 |
| #20273443 | 2 |
| #20273352 | 2 |
| #20273228 | 2 |
| #20273227 | 2 |
| C53×#1559 | 2 |
| #8495 | 53 |