Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
620 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 23. #16811352 | C4 | semidirect |
| 25. #16811351 | C4 | semidirect |
| 29. #16811348 | C4 | semidirect |
| 38. C53×#557 | C4 | semidirect |
| 267. #557 | #6157 | semidirect |
| 290. C53 | #8495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290903 | 2 |
| #20290250 | 2 |
| #20290207 | 2 |
| #20290108 | 2 |
| #20289207 | 2 |
| #8495 | 53 |