Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2222 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2222 conjugacy classes of subgroups — too many to draw. Only its 667 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 |
|---|---|---|
| 1. C2×C7×#376 | C2 | semidirect |
| 3. C2×#89700 | C2 | semidirect |
| 4. #11730875 | C2 | direct (N × H) |
| 5. C2×#89447 | C2 | semidirect |
| 6. C2×#89448 | C2 | semidirect |
| 13. C7×#376 | C22 | semidirect |
| 18. #89700 | C22 | semidirect |
| 19. #89448 | C22 | semidirect |
| 20. #89447 | C22 | semidirect |
| 47. C2×#376 | D7 | semidirect |
| 84. #376 | C2×D7 | semidirect |
| 173. C2×C7 | #2644 | semidirect |
| 203. C7 | C2×#2644 | semidirect |
| 219. C2 | #11730875 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#376 | 2 |
| C2×#89711 | 2 |
| C2×#89700 | 2 |
| #11730875 | 2 |
| C2×#89447 | 2 |
| C2×#89448 | 2 |
| C2×#2644 | 7 |