Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
404 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 2. C2×D3×C7×C8 | C2 | semidirect |
| 3. D3×C7×C4⋊C4 | C2 | semidirect |
| 4. C3×C7×#102 | C2 | semidirect |
| 5. C7×#832 | C2 | semidirect |
| 6. C7×#821 | C2 | semidirect |
| 7. C7×#809 | C2 | semidirect |
| 13. D3×C7×D4 | C4 | semidirect |
| 17. C2×C3×C7×C8 | C22 | semidirect |
| 18. C3×C7×C4⋊C4 | C22 | semidirect |
| 19. C7×C4⋊Dic3 | C22 | semidirect |
| 21. C2×C7×C3⋊C8 | C22 | semidirect |
| 29. C7×#102 | D3 | direct (N × H) |
| 30. D3×#102 | C7 | direct (N × H) |
| 38. C3×C7×D4 | C2×C4 | semidirect |
| 45. C7×D12 | C2×C4 | semidirect |
| 61. C2×C7×C8 | C2×D3 | semidirect |
| 64. C7×C4⋊C4 | C2×D3 | semidirect |
| 66. C2×D3×C8 | C2×C7 | semidirect |
| 67. D3×C4⋊C4 | C2×C7 | semidirect |
| 68. C3×#102 | C2×C7 | semidirect |
| 69. #832 | C2×C7 | semidirect |
| 70. #821 | C2×C7 | semidirect |
| 71. #809 | C2×C7 | semidirect |
| 99. C7×D4 | C4×D3 | semidirect |
| 113. D3×D4 | C4×C7 | semidirect |
| 117. C2×C3×C8 | C22×C7 | semidirect |
| 118. C3×C4⋊C4 | C22×C7 | semidirect |
| 119. C4⋊Dic3 | C22×C7 | semidirect |
| 121. C2×C3⋊C8 | C22×C7 | semidirect |
| 128. D3×C7 | #102 | direct (N × H) |
| 135. #102 | D3×C7 | direct (N × H) |
| 159. C3×D4 | C2×C4×C7 | semidirect |
| 166. D12 | C2×C4×C7 | semidirect |
| 172. C3×C7 | C2×#102 | semidirect |
| 183. C2×C8 | C2×D3×C7 | semidirect |
| 186. C4⋊C4 | C2×D3×C7 | semidirect |
| 219. D4 | C4×D3×C7 | semidirect |
| 229. C7 | D3×#102 | direct (N × H) |
| 235. D3 | C7×#102 | direct (N × H) |
| 252. C3 | C2×C7×#102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C7×D4 | 2 |
| C2×D3×C7×C8 | 2 |
| D3×C7×C4⋊C4 | 2 |
| C3×C7×#102 | 2 |
| C7×#832 | 2 |
| C7×#821 | 2 |
| C7×#809 | 2 |
| C2×C7×#102 | 3 |
| D3×#102 | 7 |