Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #20276320 | C2 | semidirect |
| 5. #20272829 | C2 | semidirect |
| 6. #20272822 | C2 | semidirect |
| 7. C53×#1951 | C2 | semidirect |
| 14. #16810438 | C4 | semidirect |
| 15. #16810435 | C4 | semidirect |
| 139. #1951 | D53 | semidirect |
| 162. C53 | #13156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276462 | 2 |
| C2×#16810432 | 2 |
| #20276320 | 2 |
| #20275613 | 2 |
| #20272829 | 2 |
| #20272822 | 2 |
| C53×#1951 | 2 |
| #13156 | 53 |