Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
670 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 670 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. C2×#16810390 | C2 | semidirect |
| 3. #20272716 | C2 | semidirect |
| 4. #20272713 | C2 | semidirect |
| 5. C2×C53×#323 | C2 | semidirect |
| 6. C2×#13133191 | C4 | semidirect |
| 9. #16810548 | C4 | semidirect |
| 13. #16810532 | C4 | semidirect |
| 16. #16810483 | C4 | semidirect |
| 23. C22×D212 | C2×C4 | semidirect |
| 33. C2×C4⋊Dic53 | C2×C4 | semidirect |
| 46. #13133124 | C2×C4 | semidirect |
| 47. #13133124 | C2×C4 | semidirect |
| 234. C2×#323 | D53 | semidirect |
| 265. C53 | #11692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20280449 | 2 |
| C2×#16810390 | 2 |
| #20272716 | 2 |
| #20272713 | 2 |
| C2×C53×#323 | 2 |
| #11692 | 53 |