Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
212 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 54 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. D16×#6157 | C2 | semidirect |
| 2. #20289877 | C2 | semidirect |
| 3. #20289864 | C2 | semidirect |
| 4. #20289821 | C2 | semidirect |
| 12. D1696 | C4 | semidirect |
| 13. #16810458 | C4 | semidirect |
| 15. C53×D32 | C4 | semidirect |
| 23. D848 | C2×C4 | semidirect |
| 26. #13133123 | C2×C4 | semidirect |
| 27. D16×C53 | C2×C4 | semidirect |
| 28. C32×C53 | C2×C4 | semidirect |
| 76. D32 | #6157 | semidirect |
| 82. C53 | #13654 | semidirect |
| 87. D16 | C2×#6157 | semidirect |
| 95. C32 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D16×#6157 | 2 |
| #20289877 | 2 |
| #20289864 | 2 |
| #20289821 | 2 |
| D32×D53 | 2 |
| #13654 | 53 |