Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1006 conjugacy classes of subgroups; only the 347 normal subgroups are shown.
This group has 1006 conjugacy classes of subgroups — too many to draw. Only its 347 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 |
|---|---|---|
| 43. C8×Dic7 | Q8 | semidirect |
| 105. C7×C8 | C4⋊Q8 | semidirect |
| 106. C7⋊C8 | C4⋊Q8 | semidirect |
| 138. Dic7 | #498 | semidirect |
| 181. C8 | #6507 | semidirect |
| 182. C7 | #33310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#498 | 2 |
| #11740698 | 2 |
| C2×#89851 | 2 |
| C2×#89452 | 2 |
| #11728308 | 2 |
| C4×C8×Dic7 | 2 |
| #33310 | 7 |