Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
342 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 52. C2×Dic106 | C16 | semidirect |
| 137. C53 | #11493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810747 | 2 |
| #20276511 | 2 |
| #20272655 | 2 |
| #20272654 | 2 |
| C53×#1322 | 2 |
| #11493 | 53 |