Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
182 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
| 89. #1426 | D53 | semidirect |
| 107. C53 | #13638 | 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 |
| #20276498 | 2 |
| #20272922 | 2 |
| #20272921 | 2 |
| #20272920 | 2 |
| C53×#1426 | 2 |
| #13638 | 53 |