Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
392 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 98 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. #20290434 | C2 | semidirect |
| 4. #20289926 | C2 | semidirect |
| 5. #20289610 | C2 | semidirect |
| 6. #20289603 | C2 | semidirect |
| 8. #16811673 | C4 | semidirect |
| 9. #16811672 | C4 | semidirect |
| 10. #16811658 | C4 | semidirect |
| 13. D4×#88324 | C4 | semidirect |
| 22. #16811480 | C4 | semidirect |
| 23. #16811478 | C4 | semidirect |
| 218. C53 | #8248 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291528 | 2 |
| #20290434 | 2 |
| #20290166 | 2 |
| #20289926 | 2 |
| #20289610 | 2 |
| #20289603 | 2 |
| #20273198 | 2 |
| #8248 | 53 |