Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
190 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 190 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. #20272922 | C2 | semidirect |
| 5. #20272921 | C2 | semidirect |
| 6. #20272920 | C2 | semidirect |
| 7. C53×#1426 | C2 | semidirect |
| 12. #16810456 | C4 | semidirect |
| 13. C32×D53 | C4 | semidirect |
| 33. #13133123 | C2×C4 | semidirect |
| 37. C32×C53 | C2×C4 | semidirect |
| 90. #1426 | D53 | direct (N × H) |
| 94. D53 | #1426 | direct (N × H) |
| 108. C53 | C2×#1426 | semidirect |
| 125. C32 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M64×D53 | 2 |
| #368×D53 | 2 |
| #367×D53 | 2 |
| #20272922 | 2 |
| #20272921 | 2 |
| #20272920 | 2 |
| C53×#1426 | 2 |
| C2×#1426 | 53 |