Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
202 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 56 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. Q32×#6157 | C2 | semidirect |
| 3. #20289877 | C2 | semidirect |
| 4. #20289865 | C2 | semidirect |
| 6. C32×#6157 | C2 | semidirect |
| 18. #16810462 | C4 | semidirect |
| 19. #16810461 | C4 | semidirect |
| 20. #16810460 | C4 | semidirect |
| 22. C53×SD64 | C4 | semidirect |
| 34. Dic424 | C2×C4 | semidirect |
| 39. #13133123 | C2×C4 | semidirect |
| 40. Q32×C53 | C2×C4 | semidirect |
| 42. C32×C53 | C2×C4 | semidirect |
| 89. #6157 | SD64 | direct (N × H) |
| 113. SD64 | #6157 | direct (N × H) |
| 121. C53 | C4×SD64 | semidirect |
| 128. Q32 | C2×#6157 | semidirect |
| 141. C32 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q32×#6157 | 2 |
| D16×#6157 | 2 |
| #20289877 | 2 |
| #20289865 | 2 |
| #20289864 | 2 |
| C32×#6157 | 2 |
| SD64×D53 | 2 |
| C4×SD64 | 53 |