Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
290 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 290 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. C2×#16810456 | C2 | semidirect |
| 3. #368×D53 | C2 | semidirect |
| 4. #20272900 | C2 | semidirect |
| 5. #20272899 | C2 | semidirect |
| 6. #20272898 | C2 | semidirect |
| 7. C53×#1417 | C2 | semidirect |
| 21. C2×#13133123 | C22 | semidirect |
| 22. #16810453 | C22 | semidirect |
| 25. C2×C32×C53 | C22 | semidirect |
| 26. C53×#368 | C22 | semidirect |
| 144. #1417 | D53 | semidirect |
| 166. C2×C32 | C2×D53 | semidirect |
| 169. #368 | C2×D53 | semidirect |
| 170. C53 | #13620 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #508×D53 | 2 |
| C2×#16810456 | 2 |
| #368×D53 | 2 |
| #20272900 | 2 |
| #20272899 | 2 |
| #20272898 | 2 |
| C53×#1417 | 2 |
| #13620 | 53 |