Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
442 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20276324 | C2 | semidirect |
| 3. #20274752 | C2 | semidirect |
| 4. #20272731 | C2 | semidirect |
| 5. #20272730 | C2 | semidirect |
| 6. #20272729 | C2 | semidirect |
| 7. C53×#1349 | C2 | semidirect |
| 21. C22⋊#11719908 | C22 | semidirect |
| 23. #16810388 | C22 | semidirect |
| 25. C53×C22⋊C16 | C22 | semidirect |
| 26. C53×#341 | C22 | semidirect |
| 187. #1349 | D53 | semidirect |
| 212. C22⋊C16 | C2×D53 | semidirect |
| 214. #341 | C2×D53 | semidirect |
| 215. C53 | #11895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #466×D53 | 2 |
| #20276324 | 2 |
| #20274752 | 2 |
| #20272731 | 2 |
| #20272730 | 2 |
| #20272729 | 2 |
| C53×#1349 | 2 |
| #11895 | 53 |