Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 82 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. D53⋊#362 | C2 | semidirect |
| 4. #20290877 | C2 | semidirect |
| 5. #20289785 | C2 | semidirect |
| 6. #20289764 | C2 | semidirect |
| 24. C2×#13133163 | C4 | semidirect |
| 25. C2×#13133162 | C4 | semidirect |
| 26. C2×#13133160 | C4 | semidirect |
| 28. C2×Q32×C53 | C4 | semidirect |
| 193. C2×Q32 | #6157 | semidirect |
| 208. C53 | #13035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291495 | 2 |
| D53⋊#362 | 2 |
| #20291031 | 2 |
| #20290877 | 2 |
| #20289785 | 2 |
| #20289764 | 2 |
| C2×#16811065 | 2 |
| #13035 | 53 |