Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
638 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 167 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 |
|---|---|---|
| 3. #20272597 | C2 | semidirect |
| 4. #20272596 | C2 | semidirect |
| 5. C53×#1295 | C2 | semidirect |
| 9. #16810678 | C4 | semidirect |
| 34. #13133128 | C2×C4 | semidirect |
| 41. #97×C53 | C2×C4 | semidirect |
| 122. #1295 | D53 | semidirect |
| 141. C53 | #8030 | semidirect |
| 162. #97 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810678 | 2 |
| #382×D53 | 2 |
| #20272597 | 2 |
| #20272596 | 2 |
| C53×#1295 | 2 |
| #8030 | 53 |