Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
760 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20275699 | C2 | semidirect |
| 4. #20273234 | C2 | semidirect |
| 5. #20272621 | C2 | semidirect |
| 6. #20272601 | C2 | semidirect |
| 8. C2×#13133247 | C4 | semidirect |
| 14. #16810624 | C4 | semidirect |
| 29. C22×Dic106 | C2×C4 | semidirect |
| 34. C2×#11719917 | C2×C4 | semidirect |
| 39. C2×C4⋊Dic53 | C2×C4 | semidirect |
| 255. C53 | #9361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283975 | 2 |
| #20275699 | 2 |
| #20274659 | 2 |
| #20273234 | 2 |
| #20272621 | 2 |
| #20272601 | 2 |
| C53×#2339 | 2 |
| #9361 | 53 |