Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
182 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 8. C2×#13133267 | C4 | semidirect |
| 14. C2×#13133123 | C4 | semidirect |
| 15. C2×C32×C53 | C4 | semidirect |
| 94. C2×C32 | #6157 | semidirect |
| 97. C53 | #7466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811556 | 2 |
| C2×#16811510 | 2 |
| C2×#16810456 | 2 |
| #7466 | 53 |