Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
454 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 32. #13133278 | C8 | semidirect |
| 113. #88324 | #101 | semidirect |
| 159. C53 | C8×#101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811672 | 2 |
| #20290468 | 2 |
| #20289916 | 2 |
| #20289559 | 2 |
| #20273037 | 2 |
| C8×#101 | 53 |