Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
182 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 111 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. #11725407 | C2 | semidirect |
| 8. C7×M64 | C4 | semidirect |
| 10. C2×C7×C32 | C4 | semidirect |
| 54. M64 | Dic7 | semidirect |
| 56. C2×C32 | Dic7 | semidirect |
| 131. C7 | #13638 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×M64 | 2 |
| C2×#89301 | 2 |
| #11729158 | 2 |
| #11725407 | 2 |
| #13638 | 7 |