Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
376 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 70 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×#6460 | C2 | semidirect |
| 3. C2×#66566 | C2 | semidirect |
| 4. C2×#66564 | C2 | semidirect |
| 5. #10620648 | C2 | semidirect |
| 6. C7×#809 | C2 | semidirect |
| 7. (C2×D7)⋊(C3⋊C8) | C2 | semidirect |
| 13. C2×C3×Dic14 | C22 | semidirect |
| 17. C3×C7×C4⋊C4 | C22 | semidirect |
| 18. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 19. C2×C7×C3⋊C8 | C22 | semidirect |
| 27. #6460 | D3 | semidirect |
| 60. C2×Dic14 | C2×D3 | semidirect |
| 62. C7×C4⋊C4 | C2×D3 | semidirect |
| 74. #809 | D7 | semidirect |
| 84. C2×C3×D7 | SD16 | semidirect |
| 122. C3×C4⋊C4 | C2×D7 | semidirect |
| 127. C2×C3⋊C8 | C2×D7 | semidirect |
| 151. C2×D7 | #215 | semidirect |
| 178. C3×C7 | #450 | semidirect |
| 192. C4⋊C4 | D3×D7 | semidirect |
| 237. C7 | #5046 | semidirect |
| 260. C3 | #89548 | 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×#6460 | 2 |
| C2×#66566 | 2 |
| C2×#66564 | 2 |
| #10620648 | 2 |
| C7×#809 | 2 |
| (C2×D7)⋊(C3⋊C8) | 2 |
| #89548 | 3 |
| #5046 | 7 |