Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1090 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 183 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×#16811066 | C2 | semidirect |
| 3. #20284370 | C2 | semidirect |
| 4. #20276668 | C2 | semidirect |
| 5. #20276452 | C2 | semidirect |
| 6. C53×#2115 | C2 | semidirect |
| 15. C22×Dic212 | C22 | semidirect |
| 18. #16811066 | C22 | semidirect |
| 21. #16810881 | C22 | semidirect |
| 23. #16810661 | C22 | semidirect |
| 25. #16810434 | C22 | semidirect |
| 27. C2×M32×C53 | C22 | semidirect |
| 28. C53×#349 | C22 | semidirect |
| 198. #2115 | D53 | semidirect |
| 219. C2×M32 | C2×D53 | semidirect |
| 225. #349 | C2×D53 | semidirect |
| 226. C53 | #33532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289489 | 2 |
| C2×#16811066 | 2 |
| #20284370 | 2 |
| #20276668 | 2 |
| #20276452 | 2 |
| C53×#2115 | 2 |
| #33532 | 53 |