Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
318 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 14. #89300 | C4 | semidirect |
| 62. C7×C16 | C4⋊C4 | semidirect |
| 150. C16 | Dic7⋊C4 | semidirect |
| 178. C7 | #13167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#366 | 2 |
| C2×#89300 | 2 |
| C2×#89297 | 2 |
| #11728365 | 2 |
| #11725528 | 2 |
| #13167 | 7 |