Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
380 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 20. #16811003 | C4 | semidirect |
| 21. #16810975 | C4 | semidirect |
| 22. #16810975 | C4 | semidirect |
| 26. C53×#498 | C4 | semidirect |
| 158. #498 | #6157 | semidirect |
| 175. C53 | #9416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291629 | 2 |
| #20290207 | 2 |
| #20290139 | 2 |
| #20290138 | 2 |
| #20289582 | 2 |
| #20289575 | 2 |
| #20285461 | 2 |
| #9416 | 53 |