Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
376 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20274761 | C2 | semidirect |
| 3. #20272704 | C2 | semidirect |
| 4. #20272701 | C2 | semidirect |
| 5. C53×#2115 | C2 | semidirect |
| 6. C2×#13133239 | C4 | semidirect |
| 8. #16810881 | C4 | semidirect |
| 10. #16810876 | C4 | semidirect |
| 15. C2×#13133149 | C4 | semidirect |
| 167. #2115 | D53 | semidirect |
| 194. C53 | #11867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284377 | 2 |
| #20274761 | 2 |
| #20272704 | 2 |
| #20272701 | 2 |
| C53×#2115 | 2 |
| #11867 | 53 |