Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
122 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 30. #11719910 | C16 | semidirect |
| 63. C53 | #7053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289630 | 2 |
| #20289627 | 2 |
| #20272634 | 2 |
| #7053 | 53 |