Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
392 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 73 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. #20276334 | C2 | semidirect |
| 3. #20274764 | C2 | semidirect |
| 4. #20272707 | C2 | semidirect |
| 5. #20272706 | C2 | semidirect |
| 6. #20272705 | C2 | semidirect |
| 7. C53×#1341 | C2 | semidirect |
| 21. #16810405 | C22 | semidirect |
| 23. #16810381 | C22 | semidirect |
| 25. C53×#349 | C22 | semidirect |
| 26. C53×#338 | C22 | semidirect |
| 188. #1341 | D53 | semidirect |
| 212. #349 | C2×D53 | semidirect |
| 214. #338 | C2×D53 | semidirect |
| 215. C53 | #11870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284361 | 2 |
| #20276334 | 2 |
| #20274764 | 2 |
| #20272707 | 2 |
| #20272706 | 2 |
| #20272705 | 2 |
| C53×#1341 | 2 |
| #11870 | 53 |