Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
450 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 107 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. C4×#13133156 | C2 | semidirect |
| 3. #20273462 | C2 | semidirect |
| 4. #20272677 | C2 | semidirect |
| 5. #20272676 | C2 | semidirect |
| 6. #20272675 | C2 | semidirect |
| 7. C53×#1331 | C2 | semidirect |
| 21. C4×#11719908 | C22 | semidirect |
| 22. #16810376 | C22 | semidirect |
| 25. C4×C16×C53 | C22 | semidirect |
| 26. C53×#335 | C22 | semidirect |
| 32. D8×D53 | C8 | semidirect |
| 172. #1331 | D53 | semidirect |
| 194. C4×C16 | C2×D53 | semidirect |
| 196. #335 | C2×D53 | semidirect |
| 198. C53 | #11593 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D53 | 2 |
| C4×#13133156 | 2 |
| #20273462 | 2 |
| #20272677 | 2 |
| #20272676 | 2 |
| #20272675 | 2 |
| C53×#1331 | 2 |
| #11593 | 53 |