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. C2×#66634 | C2 | semidirect |
| 3. C2×C7×#215 | C2 | semidirect |
| 4. C3×#6509 | C2 | semidirect |
| 5. #10620503 | C2 | semidirect |
| 6. #10620501 | C2 | semidirect |
| 7. (C2×D7)⋊(C3⋊C8) | C2 | semidirect |
| 10. C2×C3×C7×Q8 | C22 | semidirect |
| 18. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 20. C2×C7×C3⋊C8 | C22 | semidirect |
| 22. C3×C4⋊Dic7 | C22 | semidirect |
| 26. #6509 | D3 | semidirect |
| 54. C2×C7×Q8 | C2×D3 | semidirect |
| 65. C4⋊Dic7 | C2×D3 | semidirect |
| 71. C2×#215 | D7 | semidirect |
| 84. C2×C3×D7 | SD16 | semidirect |
| 114. C2×C3×Q8 | C2×D7 | semidirect |
| 127. C2×C3⋊C8 | C2×D7 | semidirect |
| 151. C2×D7 | #215 | semidirect |
| 178. C3×C7 | #450 | semidirect |
| 180. C2×Q8 | D3×D7 | semidirect |
| 237. C7 | #5046 | semidirect |
| 260. C3 | #89941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×D12 | 2 |
| C2×#66634 | 2 |
| C2×C7×#215 | 2 |
| C3×#6509 | 2 |
| #10620503 | 2 |
| #10620501 | 2 |
| (C2×D7)⋊(C3⋊C8) | 2 |
| #89941 | 3 |
| #5046 | 7 |