Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
326 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 81 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. D7×M64 | C2 | semidirect |
| 3. D7×#368 | C2 | semidirect |
| 4. C7×#1419 | C2 | semidirect |
| 5. #11725631 | C2 | semidirect |
| 6. #11725410 | C2 | semidirect |
| 7. #11725389 | C2 | semidirect |
| 18. C7×M64 | C22 | semidirect |
| 19. C7×#368 | C22 | semidirect |
| 20. #89301 | C22 | semidirect |
| 21. #89294 | C22 | semidirect |
| 59. #1419 | D7 | direct (N × H) |
| 101. M64 | C2×D7 | semidirect |
| 105. #368 | C2×D7 | semidirect |
| 205. D7 | #1419 | direct (N × H) |
| 230. C7 | C2×#1419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×D16 | 2 |
| D7×M64 | 2 |
| D7×#368 | 2 |
| C7×#1419 | 2 |
| #11725631 | 2 |
| #11725410 | 2 |
| #11725389 | 2 |
| C2×#1419 | 7 |