Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
290 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 4. #11725632 | C2 | semidirect |
| 8. C2×C7×Q32 | C4 | semidirect |
| 60. C2×Q32 | Dic7 | semidirect |
| 143. C7 | #13618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Q32 | 2 |
| #11729158 | 2 |
| C2×#89294 | 2 |
| #11725632 | 2 |
| #13618 | 7 |