Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
282 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 14. #16810451 | C4 | semidirect |
| 15. #16810449 | C4 | semidirect |
| 78. C16×C53 | C4⋊C4 | semidirect |
| 145. C53 | #13174 | semidirect |
| 201. C16 | #11719919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276503 | 2 |
| C2×#16810446 | 2 |
| #20275468 | 2 |
| #20275453 | 2 |
| #20272824 | 2 |
| #20272821 | 2 |
| C2×C53×#347 | 2 |
| #13174 | 53 |