Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
246 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 5. C4×#11719910 | C4 | semidirect |
| 35. C4×Dic53 | C16 | semidirect |
| 83. C53 | #7142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291072 | 2 |
| #20274460 | 2 |
| #7142 | 53 |