Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20275543 | C2 | semidirect |
| 3. #20273474 | C2 | semidirect |
| 4. #20273167 | C2 | semidirect |
| 5. C53×#1744 | C2 | semidirect |
| 7. #16811028 | C4 | semidirect |
| 8. #16811000 | C4 | semidirect |
| 9. #16810970 | C4 | semidirect |
| 66. C42×C53 | D8 | semidirect |
| 124. #1744 | D53 | semidirect |
| 146. C53 | #9847 | semidirect |
| 200. C42 | D424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285294 | 2 |
| #20275543 | 2 |
| #20273474 | 2 |
| #20273167 | 2 |
| C53×#1744 | 2 |
| #9847 | 53 |