Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20274751 | C2 | semidirect |
| 3. #20274742 | C2 | semidirect |
| 6. #20272620 | C2 | semidirect |
| 7. C53×#1305 | C2 | semidirect |
| 8. C2×#13133225 | C4 | semidirect |
| 17. #16810651 | C4 | semidirect |
| 18. #16810591 | C4 | semidirect |
| 20. #16810581 | C4 | semidirect |
| 212. #1305 | D53 | semidirect |
| 244. C53 | #8628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283405 | 2 |
| #20274751 | 2 |
| #20274742 | 2 |
| #20273259 | 2 |
| #20273256 | 2 |
| #20272620 | 2 |
| C53×#1305 | 2 |
| #8628 | 53 |