Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
454 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. #20278008 | C2 | semidirect |
| 4. #20272617 | C2 | semidirect |
| 5. C53×#1274 | C2 | semidirect |
| 22. #13133217 | Q8 | semidirect |
| 23. #13133214 | Q8 | semidirect |
| 140. #1274 | D53 | semidirect |
| 159. C53 | #10370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20278008 | 2 |
| #20275547 | 2 |
| #20273211 | 2 |
| #20272617 | 2 |
| C53×#1274 | 2 |
| #10370 | 53 |