Finite Group DatabasebetaFinite Group DatabasebetaOrder 2352.
208 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 64 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. C7×#4268 | C2 | semidirect |
| 2. C72×#67 | C2 | semidirect |
| 3. C2×C3×C7×Dic7 | C2 | semidirect |
| 4. C7×#4248 | C2 | semidirect |
| 5. C7×#4247 | C2 | semidirect |
| 6. C7×D21⋊C4 | C2 | semidirect |
| 7. D3×C7×Dic7 | C2 | semidirect |
| 20. C2×C7×Dic7 | D3 | semidirect |
| 24. #66686 | C7 | direct (N × H) |
| 37. #4268 | C2×C7 | semidirect |
| 40. C7×#67 | D7 | semidirect |
| 41. C7×#67 | C2×C7 | semidirect |
| 46. C2×C3×Dic7 | C2×C7 | semidirect |
| 47. #4248 | C2×C7 | semidirect |
| 48. #4247 | C2×C7 | semidirect |
| 49. D21⋊C4 | C2×C7 | semidirect |
| 50. D3×Dic7 | C2×C7 | semidirect |
| 51. C3×C72 | #41 | semidirect |
| 87. C2×Dic7 | D3×C7 | semidirect |
| 90. C72 | #235 | semidirect |
| 122. #67 | C7×D7 | semidirect |
| 128. C3×C7 | #1159 | semidirect |
| 129. C3×C7 | C7×#41 | semidirect |
| 157. C7 | #66686 | direct (N × H) |
| 158. C7 | C7×#235 | semidirect |
| 170. C3 | C7×#1159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#4268 | 2 |
| C72×#67 | 2 |
| C2×C3×C7×Dic7 | 2 |
| C7×#4248 | 2 |
| C7×#4247 | 2 |
| C7×D21⋊C4 | 2 |
| D3×C7×Dic7 | 2 |
| C7×#1159 | 3 |
| C7×#235 | 7 |
| #66686 | 7 |