Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
390 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 1. #20276987 | C2 | semidirect |
| 2. #20276760 | C2 | semidirect |
| 3. #20274204 | C2 | semidirect |
| 4. #20272758 | C2 | semidirect |
| 5. #20272682 | C2 | semidirect |
| 6. #20272673 | C2 | semidirect |
| 11. #16811003 | C22 | semidirect |
| 13. C4⋊#11719908 | C22 | semidirect |
| 15. #16810399 | C22 | semidirect |
| 16. #16810374 | C22 | semidirect |
| 199. C53 | #12326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276987 | 2 |
| #20276760 | 2 |
| #20274204 | 2 |
| #20272758 | 2 |
| #20272682 | 2 |
| #20272673 | 2 |
| C53×#3273 | 2 |
| #12326 | 53 |