Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
414 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 94 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×#16811548 | C2 | semidirect |
| 3. C2×#16811547 | C2 | semidirect |
| 5. #20289780 | C2 | semidirect |
| 6. #20289780 | C2 | semidirect |
| 23. C22⋊#11719908 | C4 | semidirect |
| 24. #16810402 | C4 | semidirect |
| 25. #16810402 | C4 | semidirect |
| 26. C53×C22⋊C16 | C4 | semidirect |
| 204. C22⋊C16 | #6157 | semidirect |
| 206. C53 | #12930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811633 | 2 |
| C2×#16811548 | 2 |
| C2×#16811547 | 2 |
| #20290594 | 2 |
| #20289780 | 2 |
| #20276324 | 2 |
| #12930 | 53 |