Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
302 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 107 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×M64 | C2 | semidirect |
| 3. C2×#89300 | C2 | semidirect |
| 4. #11725412 | C2 | direct (N × H) |
| 8. C2×Dic56 | C4 | semidirect |
| 11. #89676 | C4 | semidirect |
| 14. C2×D112 | C4 | semidirect |
| 16. C7×M64 | C22 | semidirect |
| 19. #89300 | C22 | semidirect |
| 40. Dic56 | C2×C4 | semidirect |
| 44. D112 | C2×C4 | semidirect |
| 47. C2×M64 | D7 | semidirect |
| 89. M64 | C2×D7 | semidirect |
| 183. C2×C7 | #1418 | semidirect |
| 209. C7 | C2×#1418 | semidirect |
| 225. C2 | #11725412 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89676 | 2 |
| C2×C7×M64 | 2 |
| C2×#89300 | 2 |
| #11725412 | 2 |
| C2×#1418 | 7 |