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. C2×C72×Dic3 | C2 | semidirect |
| 3. C3×C7×C22⋊D7 | C2 | semidirect |
| 4. C7×#4248 | C2 | semidirect |
| 5. C7×#4246 | C2 | semidirect |
| 6. C7×D21⋊C4 | C2 | semidirect |
| 7. C7×Dic3×D7 | C2 | semidirect |
| 18. C7×C22⋊D7 | D3 | semidirect |
| 24. #66683 | C7 | direct (N × H) |
| 37. #4268 | C2×C7 | semidirect |
| 42. C2×C7×Dic3 | D7 | semidirect |
| 43. C2×C7×Dic3 | C2×C7 | semidirect |
| 46. C3×C22⋊D7 | C2×C7 | semidirect |
| 47. #4248 | C2×C7 | semidirect |
| 48. #4246 | C2×C7 | semidirect |
| 49. D21⋊C4 | C2×C7 | semidirect |
| 50. Dic3×D7 | C2×C7 | semidirect |
| 51. C3×C72 | #41 | semidirect |
| 85. C22⋊D7 | D3×C7 | semidirect |
| 90. C72 | #237 | semidirect |
| 123. C2×Dic3 | C7×D7 | semidirect |
| 127. C3×C7 | #1157 | semidirect |
| 128. C3×C7 | C7×#41 | semidirect |
| 155. C7 | #66683 | direct (N × H) |
| 156. C7 | C7×#237 | semidirect |
| 168. C3 | C7×#1157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#4268 | 2 |
| C2×C72×Dic3 | 2 |
| C3×C7×C22⋊D7 | 2 |
| C7×#4248 | 2 |
| C7×#4246 | 2 |
| C7×D21⋊C4 | 2 |
| C7×Dic3×D7 | 2 |
| C7×#1157 | 3 |
| C7×#237 | 7 |
| #66683 | 7 |