Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
486 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 4. C2×#16810400 | C2 | semidirect |
| 5. #20274602 | C2 | semidirect |
| 6. #20272822 | C2 | semidirect |
| 7. C53×#1383 | C2 | semidirect |
| 12. #16810734 | C4 | semidirect |
| 17. #16810435 | C4 | semidirect |
| 18. #16810425 | C4 | semidirect |
| 39. #13133157 | C2×C4 | semidirect |
| 41. #13133151 | C2×C4 | semidirect |
| 53. C2×C16×C53 | C2×C4 | semidirect |
| 55. #108×C53 | C2×C4 | semidirect |
| 147. #1383 | D53 | semidirect |
| 169. C53 | #12647 | semidirect |
| 192. C2×C16 | C4×D53 | semidirect |
| 194. #108 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810734 | 2 |
| C2×#16810435 | 2 |
| #20276432 | 2 |
| C2×#16810400 | 2 |
| #20274602 | 2 |
| #20272822 | 2 |
| C53×#1383 | 2 |
| #12647 | 53 |