Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1128 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1128 conjugacy classes of subgroups — too many to draw. Only its 351 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. #20283310 | C2 | semidirect |
| 3. #20276452 | C2 | semidirect |
| 4. C2×#16810434 | C2 | semidirect |
| 5. C53×#3407 | C2 | semidirect |
| 7. #16811440 | C4 | semidirect |
| 9. #16811428 | C4 | semidirect |
| 14. #16810661 | C22 | semidirect |
| 15. C2×#13133149 | C22 | semidirect |
| 16. #16810434 | C22 | semidirect |
| 17. #16810434 | C22 | semidirect |
| 20. C2×M32×C53 | C22 | semidirect |
| 31. #13133239 | C2×C4 | semidirect |
| 33. C2×Dic212 | C2×C4 | semidirect |
| 35. C2×D424 | C2×C4 | semidirect |
| 123. #3407 | D53 | semidirect |
| 140. C2×M32 | C2×D53 | semidirect |
| 146. C53 | #33388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289489 | 2 |
| #20283310 | 2 |
| #20276452 | 2 |
| C2×#16810434 | 2 |
| C53×#3407 | 2 |
| #33388 | 53 |