Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
798 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 267 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×D8×Dic7 | C2 | semidirect |
| 3. C2×#89357 | C2 | semidirect |
| 4. #11729215 | C2 | direct (N × H) |
| 5. C2×#89300 | C2 | semidirect |
| 6. C2×#89297 | C2 | semidirect |
| 9. C2×C7×D16 | C4 | semidirect |
| 14. D8×Dic7 | C22 | semidirect |
| 18. #89357 | C22 | semidirect |
| 19. #89300 | C22 | semidirect |
| 20. #89297 | C22 | semidirect |
| 26. C2×C7×D8 | C2×C4 | semidirect |
| 35. C7×D16 | C2×C4 | semidirect |
| 36. C2×C7×C16 | C2×C4 | semidirect |
| 63. C7×D8 | C22×C4 | semidirect |
| 75. C7×C16 | C22×C4 | semidirect |
| 79. C2×D16 | Dic7 | semidirect |
| 116. C2×D8 | C2×Dic7 | semidirect |
| 125. D16 | C2×Dic7 | semidirect |
| 128. C2×C16 | C2×Dic7 | semidirect |
| 159. D8 | C22×Dic7 | semidirect |
| 172. C16 | C22×Dic7 | semidirect |
| 174. C2×C7 | #2177 | semidirect |
| 198. C7 | C2×#2177 | semidirect |
| 212. C2 | #11729215 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D16 | 2 |
| C2×D8×Dic7 | 2 |
| C2×#89357 | 2 |
| #11729215 | 2 |
| C2×#89300 | 2 |
| C2×#89297 | 2 |
| C2×#2177 | 7 |