Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20275633 | C2 | semidirect |
| 3. #20273209 | C2 | semidirect |
| 4. #20273004 | C2 | semidirect |
| 5. C4×#106×C53 | C2 | semidirect |
| 7. #16811028 | C4 | semidirect |
| 8. #16811000 | C4 | semidirect |
| 9. #16810970 | C4 | semidirect |
| 117. C8×C53 | #104 | semidirect |
| 139. C4×#106 | D53 | semidirect |
| 165. C53 | #9721 | semidirect |
| 261. C8 | #13133145 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285294 | 2 |
| #20275633 | 2 |
| #20273209 | 2 |
| #20273004 | 2 |
| C4×#106×C53 | 2 |
| #9721 | 53 |