Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1128 conjugacy classes of subgroups; only the 391 normal subgroups are shown.
This group has 1128 conjugacy classes of subgroups — too many to draw. Only its 391 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. #20287818 | C2 | semidirect |
| 2. #20283310 | C2 | semidirect |
| 3. #20276451 | C2 | semidirect |
| 4. C2×#16810433 | C2 | semidirect |
| 8. C2×#13133157 | C22 | semidirect |
| 10. #16810661 | C22 | semidirect |
| 11. C2×#13133149 | C22 | semidirect |
| 12. #16810433 | C22 | semidirect |
| 13. #16810433 | C22 | semidirect |
| 15. C53×#578 | C4 | semidirect |
| 17. C53×#576 | C4 | semidirect |
| 43. #135×C53 | C2×C4 | semidirect |
| 45. C2×Q16×C53 | C2×C4 | semidirect |
| 47. C2×D8×C53 | C2×C4 | semidirect |
| 132. #578 | Dic53 | semidirect |
| 134. #576 | Dic53 | semidirect |
| 146. C53 | #33388 | semidirect |
| 158. #135 | C2×Dic53 | semidirect |
| 160. C2×Q16 | C2×Dic53 | semidirect |
| 162. C2×D8 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287818 | 2 |
| #20283310 | 2 |
| #20276451 | 2 |
| C2×#16810433 | 2 |
| C53×#3584 | 2 |
| #33388 | 53 |