Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 89 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. C22⋊C16×D53 | C2 | semidirect |
| 3. #20274743 | C2 | semidirect |
| 4. #20272725 | C2 | semidirect |
| 5. #20272724 | C2 | semidirect |
| 6. #20272723 | C2 | semidirect |
| 7. C53×#1347 | C2 | semidirect |
| 8. C2×D8×D53 | C4 | semidirect |
| 12. #16810860 | C4 | semidirect |
| 16. #16810856 | C4 | semidirect |
| 18. #107×D53 | C4 | semidirect |
| 21. C22⋊#11719908 | C22 | semidirect |
| 23. #16810386 | C22 | semidirect |
| 25. C53×C22⋊C16 | C22 | semidirect |
| 26. C53×#340 | C22 | semidirect |
| 200. #1347 | D53 | semidirect |
| 226. C22⋊C16 | C2×D53 | semidirect |
| 228. #340 | C2×D53 | semidirect |
| 229. C53 | #11886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #466×D53 | 2 |
| C22⋊C16×D53 | 2 |
| #20274743 | 2 |
| #20272725 | 2 |
| #20272724 | 2 |
| #20272723 | 2 |
| C53×#1347 | 2 |
| #11886 | 53 |