Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
798 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 227 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×#89644 | C2 | semidirect |
| 3. C2×C7×#367 | C2 | semidirect |
| 4. C2×#89297 | C2 | semidirect |
| 5. C2×#89286 | C2 | semidirect |
| 6. #11727093 | C2 | direct (N × H) |
| 14. C2×D112 | C4 | semidirect |
| 17. #89644 | C22 | semidirect |
| 18. C7×#367 | C22 | semidirect |
| 19. #89297 | C22 | semidirect |
| 20. #89286 | C22 | semidirect |
| 31. C2×D56 | C2×C4 | semidirect |
| 35. C2×C7×C16 | C2×C4 | semidirect |
| 44. D112 | C2×C4 | semidirect |
| 48. C2×#367 | D7 | semidirect |
| 74. D56 | C22×C4 | semidirect |
| 75. C7×C16 | C22×C4 | semidirect |
| 88. #367 | C2×D7 | semidirect |
| 128. C2×C16 | C4×D7 | semidirect |
| 172. C16 | C2×C4×D7 | semidirect |
| 173. C2×C7 | #2177 | semidirect |
| 198. C7 | C2×#2177 | semidirect |
| 212. C2 | #11727093 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D112 | 2 |
| C2×#89644 | 2 |
| C2×C7×#367 | 2 |
| C2×#89297 | 2 |
| C2×#89286 | 2 |
| #11727093 | 2 |
| C2×#2177 | 7 |