Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
396 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 396 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. #20274760 | C2 | semidirect |
| 4. #20272701 | C2 | semidirect |
| 5. #20272700 | C2 | semidirect |
| 6. #20272699 | C2 | semidirect |
| 7. C53×#1339 | C2 | semidirect |
| 8. C2×D8×D53 | C4 | semidirect |
| 12. #16810877 | C4 | semidirect |
| 14. #16810873 | C4 | semidirect |
| 18. #16810658 | C4 | semidirect |
| 21. #16810405 | C22 | semidirect |
| 23. #16810380 | C22 | semidirect |
| 25. C53×#349 | C22 | semidirect |
| 26. C53×H(3,ℤ/4) | C22 | semidirect |
| 190. #1339 | D53 | semidirect |
| 214. #349 | C2×D53 | semidirect |
| 216. H(3,ℤ/4) | C2×D53 | semidirect |
| 217. C53 | #11868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284361 | 2 |
| #20276334 | 2 |
| #20274760 | 2 |
| #20272701 | 2 |
| #20272700 | 2 |
| #20272699 | 2 |
| C53×#1339 | 2 |
| #11868 | 53 |