Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
490 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
| 140. C2×#6157 | Q32 | semidirect |
| 214. C2×Q32 | #6157 | semidirect |
| 227. C53 | #13015 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×#6157 | 2 |
| C2×#16811536 | 2 |
| #20290861 | 2 |
| #20289773 | 2 |
| (C2×#6157)⋊C16 | 2 |
| C2×Q32×D53 | 2 |
| #13015 | 53 |