Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
712 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20283161 | C2 | semidirect |
| 3. #20274658 | C2 | semidirect |
| 4. #20273231 | C2 | semidirect |
| 5. #20272591 | C2 | semidirect |
| 6. #20272561 | C2 | semidirect |
| 7. C53×#1471 | C2 | semidirect |
| 9. C22×#11719923 | C4 | semidirect |
| 10. C22×#11719922 | C4 | semidirect |
| 18. C2×#13133140 | C4 | semidirect |
| 19. C2×#13133137 | C4 | semidirect |
| 276. #1471 | D53 | semidirect |
| 314. C53 | #9241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810766 | 2 |
| #20283161 | 2 |
| #20274658 | 2 |
| #20273231 | 2 |
| #20272591 | 2 |
| #20272561 | 2 |
| C53×#1471 | 2 |
| #9241 | 53 |