Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
516 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 86 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. #20291643 | C2 | semidirect |
| 2. #20290848 | C2 | semidirect |
| 3. C4×#13133281 | C2 | semidirect |
| 4. #20290036 | C2 | semidirect |
| 5. #20289601 | C2 | semidirect |
| 6. #20289542 | C2 | semidirect |
| 25. #16810915 | C4 | semidirect |
| 26. #16810824 | C4 | semidirect |
| 27. #16810818 | C4 | semidirect |
| 32. C53×#476 | C4 | semidirect |
| 147. D4×C53 | #104 | semidirect |
| 228. #476 | #6157 | semidirect |
| 249. C53 | #8969 | semidirect |
| 370. D4 | #13133282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291643 | 2 |
| #20290848 | 2 |
| C4×#13133281 | 2 |
| #20290036 | 2 |
| #20289601 | 2 |
| #20289542 | 2 |
| #20284777 | 2 |
| #8969 | 53 |