Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
404 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 102 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. C3×D7×C4⋊C4 | C2 | semidirect |
| 3. C2×D7×C3⋊C8 | C2 | semidirect |
| 4. #10620648 | C2 | semidirect |
| 5. C7×#809 | C2 | semidirect |
| 6. #10620503 | C2 | semidirect |
| 7. #10620501 | C2 | semidirect |
| 16. D7×D12 | C4 | semidirect |
| 17. C3×C7×C4⋊C4 | C22 | semidirect |
| 18. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 19. C2×C7×C3⋊C8 | C22 | semidirect |
| 20. C3×C4⋊Dic7 | C22 | semidirect |
| 25. D7×C4⋊C4 | D3 | semidirect |
| 40. D84 | C2×C4 | semidirect |
| 42. C7×D12 | C2×C4 | semidirect |
| 60. C7×C4⋊C4 | C2×D3 | semidirect |
| 61. C4⋊Dic7 | C2×D3 | semidirect |
| 71. #809 | D7 | direct (N × H) |
| 119. C3×C4⋊C4 | C2×D7 | semidirect |
| 122. C2×C3⋊C8 | C2×D7 | semidirect |
| 127. C3×D7 | #102 | semidirect |
| 169. D12 | C4×D7 | semidirect |
| 172. C3×C7 | C2×#102 | semidirect |
| 186. C4⋊C4 | D3×D7 | semidirect |
| 192. D7 | #809 | direct (N × H) |
| 229. C7 | C2×#809 | semidirect |
| 252. C3 | D7×#102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×D12 | 2 |
| C3×D7×C4⋊C4 | 2 |
| C2×D7×C3⋊C8 | 2 |
| #10620648 | 2 |
| C7×#809 | 2 |
| #10620503 | 2 |
| #10620501 | 2 |
| D7×#102 | 3 |
| C2×#809 | 7 |