Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
820 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20273435 | C2 | semidirect |
| 3. #20273350 | C2 | semidirect |
| 4. #20273222 | C2 | semidirect |
| 5. C53×#1963 | C2 | semidirect |
| 7. #16811339 | C4 | semidirect |
| 10. #16811258 | C4 | semidirect |
| 14. #16810680 | C22 | semidirect |
| 20. C53×#423 | C22 | semidirect |
| 22. C53×#376 | C22 | semidirect |
| 151. #1963 | D53 | semidirect |
| 170. #423 | C2×D53 | semidirect |
| 172. #376 | C2×D53 | semidirect |
| 177. C53 | #8491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289120 | 2 |
| #20273435 | 2 |
| #20273350 | 2 |
| #20273222 | 2 |
| C53×#1963 | 2 |
| #8491 | 53 |