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. C72×D12 | C2 | semidirect |
| 3. C3×C4×C7×D7 | C2 | semidirect |
| 4. C7×#4245 | C2 | semidirect |
| 5. D3×C7×Dic7 | C2 | semidirect |
| 15. C4×C7×D7 | D3 | semidirect |
| 18. #66676 | C7 | direct (N × H) |
| 28. Dic42 | C2×C7 | semidirect |
| 31. C7×D12 | D7 | semidirect |
| 32. C7×D12 | C2×C7 | semidirect |
| 35. C3×C4×D7 | C2×C7 | semidirect |
| 36. #4245 | C2×C7 | semidirect |
| 37. D3×Dic7 | C2×C7 | semidirect |
| 38. C3×C72 | #41 | semidirect |
| 65. C4×D7 | D3×C7 | semidirect |
| 67. C72 | #235 | semidirect |
| 91. D12 | C7×D7 | semidirect |
| 95. C3×C7 | #1159 | semidirect |
| 96. C3×C7 | C7×#41 | semidirect |
| 117. C7 | #66676 | direct (N × H) |
| 118. C7 | C7×#235 | semidirect |
| 127. C3 | C7×#1159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×Dic42 | 2 |
| C72×D12 | 2 |
| C3×C4×C7×D7 | 2 |
| C7×#4245 | 2 |
| D3×C7×Dic7 | 2 |
| C7×#1159 | 3 |
| C7×#235 | 7 |
| #66676 | 7 |