Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
430 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 3. C2×#16811510 | C2 | semidirect |
| 4. #20290520 | C2 | semidirect |
| 5. #20289777 | C2 | semidirect |
| 6. #20289774 | C2 | semidirect |
| 10. #16811667 | C4 | semidirect |
| 12. #16811665 | C4 | semidirect |
| 18. #16811536 | C4 | semidirect |
| 19. #16811535 | C4 | semidirect |
| 25. #16810431 | C4 | semidirect |
| 26. #16810430 | C4 | semidirect |
| 27. #16810429 | C4 | semidirect |
| 28. C53×#359 | C4 | semidirect |
| 201. #359 | #6157 | semidirect |
| 206. C53 | #12642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#443 | 2 |
| #20291022 | 2 |
| C2×#16811510 | 2 |
| #20290520 | 2 |
| #20289777 | 2 |
| #20289774 | 2 |
| #359×D53 | 2 |
| #12642 | 53 |