Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
202 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 3. #20272916 | C2 | semidirect |
| 4. #20272896 | C2 | semidirect |
| 6. C4×#13133123 | C2 | semidirect |
| 7. C4×Q32×C53 | C2 | semidirect |
| 10. #16810460 | C4 | direct (N × H) |
| 27. #13133123 | C2×C4 | semidirect |
| 31. Q32×C53 | C2×C4 | semidirect |
| 78. C4×C53 | SD64 | semidirect |
| 83. C4×Q32 | D53 | semidirect |
| 105. C53 | C4×SD64 | semidirect |
| 111. Q32 | C4×D53 | semidirect |
| 164. C4 | #16810460 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810460 | 2 |
| C4×D848 | 2 |
| #20272916 | 2 |
| #20272896 | 2 |
| #20272892 | 2 |
| C4×#13133123 | 2 |
| C4×Q32×C53 | 2 |
| C4×SD64 | 53 |