Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
286 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 4. #20272909 | C2 | semidirect |
| 5. #20272908 | C2 | semidirect |
| 6. #20272907 | C2 | semidirect |
| 7. C53×#1420 | C2 | semidirect |
| 121. #1420 | D53 | direct (N × H) |
| 125. D53 | #1420 | direct (N × H) |
| 143. C53 | C2×#1420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D53 | 2 |
| M64×D53 | 2 |
| #368×D53 | 2 |
| #20272909 | 2 |
| #20272908 | 2 |
| #20272907 | 2 |
| C53×#1420 | 2 |
| C2×#1420 | 53 |