Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
308 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 14. #16811548 | C4 | semidirect |
| 15. #16811547 | C4 | semidirect |
| 16. #16811510 | C4 | semidirect |
| 17. C16×#6157 | C4 | semidirect |
| 23. #16810447 | C4 | semidirect |
| 24. #16810446 | C4 | semidirect |
| 25. #16810445 | C4 | semidirect |
| 26. C53×#365 | C4 | semidirect |
| 160. #365 | #6157 | semidirect |
| 165. C53 | #12668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291063 | 2 |
| M32×#6157 | 2 |
| #20290520 | 2 |
| #20290518 | 2 |
| #20289784 | 2 |
| #20289782 | 2 |
| #20276486 | 2 |
| #12668 | 53 |