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×Dic42 | C2 | semidirect |
| 2. C4×D3×C72 | C2 | semidirect |
| 3. C3×C7×D28 | C2 | semidirect |
| 4. C7×#4245 | C2 | semidirect |
| 5. C7×Dic3×D7 | C2 | semidirect |
| 14. C7×D28 | D3 | semidirect |
| 18. #66669 | C7 | direct (N × H) |
| 28. Dic42 | C2×C7 | semidirect |
| 32. C4×D3×C7 | D7 | semidirect |
| 33. C4×D3×C7 | C2×C7 | semidirect |
| 35. C3×D28 | C2×C7 | semidirect |
| 36. #4245 | C2×C7 | semidirect |
| 37. Dic3×D7 | C2×C7 | semidirect |
| 38. C3×C72 | #41 | semidirect |
| 65. D28 | D3×C7 | semidirect |
| 68. C72 | #237 | semidirect |
| 94. C4×D3 | C7×D7 | semidirect |
| 97. C3×C7 | #1157 | semidirect |
| 98. C3×C7 | C7×#41 | semidirect |
| 119. C7 | #66669 | direct (N × H) |
| 120. C7 | C7×#237 | semidirect |
| 129. C3 | C7×#1157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×Dic42 | 2 |
| C4×D3×C72 | 2 |
| C3×C7×D28 | 2 |
| C7×#4245 | 2 |
| C7×Dic3×D7 | 2 |
| C7×#1157 | 3 |
| C7×#237 | 7 |
| #66669 | 7 |