Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
412 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 100 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×#16811513 | C2 | semidirect |
| 4. #20290536 | C2 | semidirect |
| 5. #20289792 | C2 | semidirect |
| 6. #20289785 | C2 | semidirect |
| 18. #16811542 | C4 | semidirect |
| 19. #16811541 | C4 | semidirect |
| 25. #16810431 | C4 | semidirect |
| 26. #16810430 | C4 | semidirect |
| 27. #16810429 | C4 | semidirect |
| 28. C53×#359 | C4 | semidirect |
| 200. #359 | #6157 | semidirect |
| 203. C53 | #12651 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#444 | 2 |
| #20291042 | 2 |
| C2×#16811513 | 2 |
| #20290536 | 2 |
| #20289792 | 2 |
| #20289785 | 2 |
| #20276441 | 2 |
| #12651 | 53 |