Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
352 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20276515 | C2 | semidirect |
| 3. #20274607 | C2 | semidirect |
| 4. #20272728 | C2 | semidirect |
| 5. #20272726 | C2 | semidirect |
| 9. #16811024 | C4 | semidirect |
| 10. #16811006 | C4 | semidirect |
| 14. #16810717 | C4 | semidirect |
| 16. D8×Dic53 | C4 | semidirect |
| 188. C53 | #11746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285280 | 2 |
| #20276515 | 2 |
| #20274607 | 2 |
| #20272728 | 2 |
| #20272726 | 2 |
| #20272724 | 2 |
| C53×#1347 | 2 |
| #11746 | 53 |