Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20283583 | C2 | semidirect |
| 5. #20272816 | C2 | semidirect |
| 6. #20272802 | C2 | semidirect |
| 7. C53×#2141 | C2 | semidirect |
| 12. C2×#13133163 | C4 | semidirect |
| 13. C2×#13133160 | C4 | semidirect |
| 166. #2141 | D53 | semidirect |
| 194. C53 | #13034 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811064 | 2 |
| #20283583 | 2 |
| #20276452 | 2 |
| #20275611 | 2 |
| #20272816 | 2 |
| #20272802 | 2 |
| C53×#2141 | 2 |
| #13034 | 53 |