Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
294 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 103 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. C7×#2158 | C2 | semidirect |
| 3. C2×#89294 | C2 | semidirect |
| 4. #11725386 | C2 | semidirect |
| 8. C2×Dic56 | C4 | semidirect |
| 11. #89676 | C4 | semidirect |
| 14. C2×D112 | C4 | semidirect |
| 15. C7×#367 | C22 | semidirect |
| 18. #89294 | C22 | semidirect |
| 48. #2158 | D7 | semidirect |
| 91. #367 | C2×D7 | semidirect |
| 207. C7 | #13622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89676 | 2 |
| C7×#2158 | 2 |
| C2×#89294 | 2 |
| #11725386 | 2 |
| #13622 | 7 |