Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
712 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 712 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 |
|---|---|---|
| 1. #20276232 | C2 | semidirect |
| 2. #20276230 | C2 | semidirect |
| 3. #20276114 | C2 | semidirect |
| 4. #20276113 | C2 | semidirect |
| 5. #20276112 | C2 | semidirect |
| 7. C53×#2069 | C2 | semidirect |
| 9. #16810672 | C22 | semidirect |
| 10. #16810671 | C22 | semidirect |
| 11. #16810671 | C22 | semidirect |
| 17. #16810381 | C22 | semidirect |
| 18. C53×#430 | C22 | semidirect |
| 20. C53×#338 | C22 | semidirect |
| 113. #2069 | D53 | semidirect |
| 124. #430 | C2×D53 | semidirect |
| 132. #338 | C2×D53 | semidirect |
| 133. C53 | #32875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276232 | 2 |
| #20276230 | 2 |
| #20276114 | 2 |
| #20276113 | 2 |
| #20276112 | 2 |
| #20274634 | 2 |
| C53×#2069 | 2 |
| #32875 | 53 |