Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
700 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 102 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. #20290894 | C2 | semidirect |
| 3. #20290232 | C2 | semidirect |
| 4. #20290225 | C2 | semidirect |
| 5. #20290097 | C2 | semidirect |
| 22. #16811351 | C4 | semidirect |
| 24. #16811347 | C4 | semidirect |
| 25. #16811346 | C4 | semidirect |
| 38. C53×#557 | C4 | semidirect |
| 297. #557 | #6157 | semidirect |
| 326. C53 | #8427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290894 | 2 |
| #20290590 | 2 |
| #20290232 | 2 |
| #20290225 | 2 |
| #20290097 | 2 |
| #20290013 | 2 |
| #20288598 | 2 |
| #8427 | 53 |