Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
682 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20276119 | C2 | semidirect |
| 3. #20272536 | C2 | semidirect |
| 4. #20272535 | C2 | semidirect |
| 5. C53×#2093 | C2 | semidirect |
| 13. #16810378 | C22 | semidirect |
| 17. C53×#384 | C22 | semidirect |
| 18. C53×#336 | C22 | semidirect |
| 158. #2093 | D53 | semidirect |
| 178. #384 | C2×D53 | semidirect |
| 181. #336 | C2×D53 | semidirect |
| 182. C53 | #7786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20281050 | 2 |
| #20276119 | 2 |
| #20272536 | 2 |
| #20272535 | 2 |
| C53×#2093 | 2 |
| #7786 | 53 |