Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
394 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 394 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. #20276511 | C2 | semidirect |
| 3. #20274607 | C2 | semidirect |
| 4. #20272725 | C2 | semidirect |
| 5. #20272724 | C2 | semidirect |
| 6. #20272723 | C2 | semidirect |
| 7. C53×#1347 | C2 | semidirect |
| 9. #16811027 | C4 | semidirect |
| 10. #16810998 | C4 | semidirect |
| 14. D8×Dic53 | C4 | semidirect |
| 15. #16810705 | C4 | semidirect |
| 172. #1347 | D53 | semidirect |
| 199. C53 | #11742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285289 | 2 |
| #20276511 | 2 |
| #20274607 | 2 |
| #20272725 | 2 |
| #20272724 | 2 |
| #20272723 | 2 |
| C53×#1347 | 2 |
| #11742 | 53 |