Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 22. C2×Dic424 | C4 | semidirect |
| 23. C2×#13133163 | C4 | semidirect |
| 24. C2×#13133163 | C4 | semidirect |
| 28. C2×Q32×C53 | C4 | semidirect |
| 194. C2×Q32 | #6157 | semidirect |
| 207. C53 | #13020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291476 | 2 |
| D53⋊#362 | 2 |
| #20291025 | 2 |
| #20290877 | 2 |
| #20289777 | 2 |
| #20289768 | 2 |
| C2×Q32×D53 | 2 |
| #13020 | 53 |