Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
522 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 1. #20290451 | C2 | semidirect |
| 2. C8×C22⋊#6157 | C2 | semidirect |
| 5. #20289597 | C2 | semidirect |
| 6. #20289595 | C2 | semidirect |
| 16. #16811477 | C4 | semidirect |
| 17. #16811477 | C4 | semidirect |
| 18. #16811474 | C4 | semidirect |
| 19. #16811474 | C4 | semidirect |
| 26. #16810651 | C4 | semidirect |
| 27. #16810590 | C4 | semidirect |
| 29. #16810578 | C4 | semidirect |
| 30. C2×#131×C53 | C4 | semidirect |
| 216. C2×#131 | #6157 | semidirect |
| 239. C53 | #8240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290451 | 2 |
| C8×C22⋊#6157 | 2 |
| #20290090 | 2 |
| #20289597 | 2 |
| #20289595 | 2 |
| #20283407 | 2 |
| #8240 | 53 |