Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
414 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. C2×#16810443 | C2 | semidirect |
| 5. #20274876 | C2 | semidirect |
| 6. #20272815 | C2 | semidirect |
| 7. C53×#1383 | C2 | semidirect |
| 12. #16810739 | C4 | semidirect |
| 151. #1383 | D53 | semidirect |
| 173. C53 | #12824 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810739 | 2 |
| C2×#16810443 | 2 |
| C2×#16810434 | 2 |
| C2×#16810432 | 2 |
| #20274876 | 2 |
| #20272815 | 2 |
| C53×#1383 | 2 |
| #12824 | 53 |