Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
426 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 1. #20280126 | C2 | semidirect |
| 4. #20272744 | C2 | semidirect |
| 5. #20272720 | C2 | semidirect |
| 6. #20272649 | C2 | semidirect |
| 211. C53 | #12197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20280126 | 2 |
| #20273718 | 2 |
| #20273684 | 2 |
| #20272744 | 2 |
| #20272720 | 2 |
| #20272649 | 2 |
| C53×#2007 | 2 |
| #12197 | 53 |