Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
182 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 59 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. #20276586 | C2 | semidirect |
| 4. #20272922 | C2 | semidirect |
| 6. #20272850 | C2 | semidirect |
| 7. C53×#1420 | C2 | semidirect |
| 11. #16810463 | C4 | semidirect |
| 12. #16810460 | C4 | semidirect |
| 85. #1420 | D53 | semidirect |
| 104. C53 | #13657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277033 | 2 |
| #20276600 | 2 |
| #20276586 | 2 |
| #20272922 | 2 |
| #20272903 | 2 |
| #20272850 | 2 |
| C53×#1420 | 2 |
| #13657 | 53 |