Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
568 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20273029 | C2 | semidirect |
| 3. #20272711 | C2 | semidirect |
| 4. C53×#1740 | C2 | semidirect |
| 5. C2×#13133214 | C4 | semidirect |
| 9. #16810540 | C4 | semidirect |
| 13. #16810489 | C4 | semidirect |
| 171. #1740 | D53 | semidirect |
| 197. C53 | #11693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20280465 | 2 |
| #20273029 | 2 |
| #20272711 | 2 |
| C53×#1740 | 2 |
| #11693 | 53 |