Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
194 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. C2×Dic848 | C2 | semidirect |
| 3. #20272915 | C2 | semidirect |
| 4. #20272897 | C2 | semidirect |
| 57. C22×C53 | Q64 | semidirect |
| 82. C53 | #13695 | semidirect |
| 124. C22 | Dic848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic848 | 2 |
| #20276806 | 2 |
| #20272915 | 2 |
| #20272897 | 2 |
| C22×C32×C53 | 2 |
| #13695 | 53 |