Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
294 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 294 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 |
|---|---|---|
| 2. #11729158 | C2 | semidirect |
| 3. C2×#89294 | C2 | semidirect |
| 4. #11725634 | C2 | semidirect |
| 8. C7×#508 | C4 | semidirect |
| 10. C2×C7×Q32 | C4 | semidirect |
| 12. C2×C7×D16 | C4 | semidirect |
| 15. #89300 | C22 | semidirect |
| 18. #89294 | C22 | semidirect |
| 81. #508 | Dic7 | semidirect |
| 83. C2×Q32 | Dic7 | semidirect |
| 85. C2×D16 | Dic7 | 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×C7×#508 | 2 |
| #11729158 | 2 |
| C2×#89294 | 2 |
| #11725634 | 2 |
| #13622 | 7 |