Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
438 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 15. C2×Dic56 | C4 | semidirect |
| 105. C2×Dic7 | Q32 | semidirect |
| 209. C7 | #13236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic56 | 2 |
| C2×C7×#366 | 2 |
| C2×C16×Dic7 | 2 |
| #11728381 | 2 |
| C2×#89287 | 2 |
| #13236 | 7 |