Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
704 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 704 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. #20274653 | C2 | semidirect |
| 4. #20273075 | C2 | semidirect |
| 5. #20272621 | C2 | semidirect |
| 6. #20272603 | C2 | semidirect |
| 7. C53×#1519 | C2 | semidirect |
| 9. C2×#13133243 | C4 | semidirect |
| 10. C2×#13133243 | C4 | semidirect |
| 16. #16810622 | C4 | semidirect |
| 17. #16810622 | C4 | semidirect |
| 274. #1519 | D53 | semidirect |
| 313. C53 | #9347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283965 | 2 |
| #20283161 | 2 |
| #20274653 | 2 |
| #20273075 | 2 |
| #20272621 | 2 |
| #20272603 | 2 |
| C53×#1519 | 2 |
| #9347 | 53 |