Finite Group DatabasebetaFinite Group DatabasebetaOrder 1008.
248 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C7 | D32 |
| commutator, cosocle | C2×C32 | C23×C7 |
| Frattini | C2 | C2×D32×C7 |
| Fitting, socle | C22×C32×C7 | C22 |
| hypocenter | C32 | C2×C7×D4 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C22×C7 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C7×C3⋊D3 | C2 | semidirect |
| 2. C22×C3×D3×C7 | C2 | semidirect |
| 3. C2×C3×C7×Dic3 | C2 | semidirect |
| 4. C7×#626 | C2 | direct (N × H) |
| 9. C2×C7×C3⋊D3 | C22 | semidirect |
| 11. C2×C3×D3×C7 | C22 | semidirect |
| 12. C3×C7×Dic3 | C22 | semidirect |
| 17. C22×D3×C7 | D3 | semidirect |
| 20. C2×C7×Dic3 | D3 | semidirect |
| 22. C2×#626 | C7 | direct (N × H) |
| 23. C2×C32×C7 | D4 | semidirect |
| 40. C2×D3×C7 | C2×D3 | semidirect |
| 42. C7×Dic3 | C2×D3 | semidirect |
| 43. C22×C3⋊D3 | C2×C7 | semidirect |
| 44. C22×C3×D3 | C2×C7 | semidirect |
| 45. C2×C3×Dic3 | C2×C7 | semidirect |
| 46. #626 | C2×C7 | direct (N × H) |
| 47. C32×C7 | C2×D4 | semidirect |
| 57. C2×C3×C7 | D12 | semidirect |
| 58. C2×C3×C7 | #67 | semidirect |
| 67. C2×C3⋊D3 | C22×C7 | semidirect |
| 69. C2×C3×D3 | C22×C7 | semidirect |
| 70. C3×Dic3 | C22×C7 | semidirect |
| 81. C22×D3 | D3×C7 | semidirect |
| 84. C2×Dic3 | D3×C7 | semidirect |
| 87. C3×C7 | C2×D12 | semidirect |
| 88. C3×C7 | C2×#67 | semidirect |
| 89. C2×C32 | C7×D4 | semidirect |
| 96. C2×C7 | #626 | direct (N × H) |
| 110. C2×D3 | C2×D3×C7 | semidirect |
| 112. Dic3 | C2×D3×C7 | semidirect |
| 113. C32 | C2×C7×D4 | semidirect |
| 118. C7 | C2×#626 | direct (N × H) |
| 122. C2×C3 | C7×D12 | semidirect |
| 123. C2×C3 | C7×#67 | semidirect |
| 137. C3 | C2×C7×D12 | semidirect |
| 138. C3 | C2×C7×#67 | semidirect |
| 141. C2 | C7×#626 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×C3⋊D3 | 2 |
| C22×C3×D3×C7 | 2 |
| C2×C3×C7×Dic3 | 2 |
| C7×#626 | 2 |
| C2×C7×#67 | 3 |
| C2×C7×D12 | 3 |
| C2×#626 | 7 |