Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
712 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #20272740 | C2 | direct (N × H) |
| 5. C22×C4⋊Dic53 | C4 | semidirect |
| 11. #16810559 | C4 | semidirect |
| 13. C2×#13133124 | C4 | semidirect |
| 26. C2×C4⋊Dic53 | C2×C4 | semidirect |
| 38. #13133124 | C2×C4 | semidirect |
| 201. C2×C53 | #1352 | semidirect |
| 220. C53 | C2×#1352 | semidirect |
| 397. C2 | #20272740 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810559 | 2 |
| C2×#16810390 | 2 |
| #20272740 | 2 |
| C2×C53×#323 | 2 |
| C2×#1352 | 53 |