Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20275634 | C2 | semidirect |
| 3. C4×#13133149 | C2 | semidirect |
| 4. #20273211 | C2 | semidirect |
| 5. C53×#1451 | C2 | semidirect |
| 7. #16811028 | C4 | semidirect |
| 8. #16811000 | C4 | semidirect |
| 9. #16810970 | C4 | semidirect |
| 119. C8×C53 | #104 | semidirect |
| 141. #1451 | D53 | semidirect |
| 165. C53 | #9721 | semidirect |
| 261. C8 | #13133143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285294 | 2 |
| #20275634 | 2 |
| C4×#13133149 | 2 |
| #20273211 | 2 |
| C53×#1451 | 2 |
| #9721 | 53 |