Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
510 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 510 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 |
|---|---|---|
| 2. C2×C7×#366 | C2 | semidirect |
| 3. C2×C16×Dic7 | C2 | semidirect |
| 4. #11728382 | C2 | semidirect |
| 5. C2×#89286 | C2 | semidirect |
| 15. C2×D112 | C4 | semidirect |
| 45. C2×#366 | D7 | semidirect |
| 77. C7×C16 | C22⋊C4 | semidirect |
| 108. C2×Dic7 | D16 | semidirect |
| 187. C16 | (C2×D7)⋊C4 | semidirect |
| 220. C7 | #13235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D112 | 2 |
| C2×C7×#366 | 2 |
| C2×C16×Dic7 | 2 |
| #11728382 | 2 |
| C2×#89286 | 2 |
| #13235 | 7 |