Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
212 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 65 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. D16×Dic53 | C2 | semidirect |
| 3. #20276561 | C2 | semidirect |
| 4. #20272916 | C2 | semidirect |
| 5. #20272894 | C2 | semidirect |
| 6. #20272848 | C2 | semidirect |
| 7. C53×#1415 | C2 | semidirect |
| 11. #16810458 | C4 | semidirect |
| 24. D848 | C2×C4 | semidirect |
| 30. #13133123 | C2×C4 | semidirect |
| 33. D16×C53 | C2×C4 | semidirect |
| 90. #1415 | D53 | semidirect |
| 109. C53 | #13654 | semidirect |
| 117. D16 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810458 | 2 |
| D16×Dic53 | 2 |
| #20276561 | 2 |
| #20272916 | 2 |
| #20272894 | 2 |
| #20272848 | 2 |
| C53×#1415 | 2 |
| #13654 | 53 |