Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#16811039 | C2 | semidirect |
| 3. #20276450 | C2 | semidirect |
| 4. C2×#16810431 | C2 | semidirect |
| 5. #20274766 | C2 | semidirect |
| 6. #20272828 | C2 | semidirect |
| 7. C53×#1382 | C2 | semidirect |
| 16. #16810899 | C4 | semidirect |
| 17. #16810894 | C4 | semidirect |
| 181. #1382 | D53 | semidirect |
| 209. C53 | #13071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811039 | 2 |
| #20284436 | 2 |
| #20276450 | 2 |
| C2×#16810431 | 2 |
| #20274766 | 2 |
| #20272828 | 2 |
| C53×#1382 | 2 |
| #13071 | 53 |