Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
530 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20277358 | C2 | semidirect |
| 3. #20275634 | C2 | semidirect |
| 4. #20273224 | C2 | semidirect |
| 5. #20272609 | C2 | semidirect |
| 6. #20272570 | C2 | semidirect |
| 7. C53×#1490 | C2 | semidirect |
| 10. #16810913 | C4 | semidirect |
| 11. #16810818 | C4 | semidirect |
| 190. #1490 | D53 | semidirect |
| 221. C53 | #9329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284806 | 2 |
| #20277358 | 2 |
| #20275634 | 2 |
| #20273224 | 2 |
| #20272609 | 2 |
| #20272570 | 2 |
| C53×#1490 | 2 |
| #9329 | 53 |