Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
474 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×#16811663 | C2 | semidirect |
| 2. C2×#16811542 | C2 | semidirect |
| 5. #20289780 | C2 | semidirect |
| 6. #20289755 | C2 | semidirect |
| 24. C2×#13133163 | C4 | semidirect |
| 25. C2×#13133162 | C4 | semidirect |
| 26. C2×#13133160 | C4 | semidirect |
| 28. C2×Q32×C53 | C4 | semidirect |
| 202. C2×Q32 | #6157 | semidirect |
| 217. C53 | #13038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811663 | 2 |
| C2×#16811542 | 2 |
| C2×#16811540 | 2 |
| #20290869 | 2 |
| #20289780 | 2 |
| #20289755 | 2 |
| C2×#16811065 | 2 |
| #13038 | 53 |