Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
934 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 1. #20283739 | C2 | semidirect |
| 3. #20274645 | C2 | semidirect |
| 4. #20272582 | C2 | semidirect |
| 5. C53×#1799 | C2 | semidirect |
| 14. #16810540 | C4 | semidirect |
| 15. #16810532 | C4 | semidirect |
| 31. C22×#88322 | D4 | semidirect |
| 121. C23×C53 | #102 | semidirect |
| 158. C2×C4×C53 | #102 | semidirect |
| 208. #1799 | D53 | semidirect |
| 237. C53 | #9468 | semidirect |
| 350. C23 | #13133137 | semidirect |
| 381. C2×C4 | #13133137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283739 | 2 |
| #20278071 | 2 |
| #20274645 | 2 |
| #20272582 | 2 |
| C53×#1799 | 2 |
| #9468 | 53 |