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. C7×#946 | C2 | semidirect |
| 4. C2×C3×#1143 | C2 | semidirect |
| 5. #10620504 | C2 | semidirect |
| 6. #10620499 | C2 | semidirect |
| 7. (C2×D3)⋊(C7⋊C8) | C2 | semidirect |
| 10. C2×C3×C7×Q8 | C22 | semidirect |
| 18. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 20. C7×C4⋊Dic3 | C22 | semidirect |
| 23. C2×C3×C7⋊C8 | C22 | semidirect |
| 27. C2×#1143 | D3 | semidirect |
| 54. C2×C7×Q8 | C2×D3 | semidirect |
| 67. C2×C7⋊C8 | C2×D3 | semidirect |
| 70. #946 | D7 | semidirect |
| 81. C2×D3×C7 | SD16 | semidirect |
| 114. C2×C3×Q8 | C2×D7 | semidirect |
| 125. C4⋊Dic3 | C2×D7 | semidirect |
| 178. C3×C7 | #450 | semidirect |
| 180. C2×Q8 | D3×D7 | semidirect |
| 210. C2×D3 | #1143 | semidirect |
| 237. C7 | #5169 | semidirect |
| 260. C3 | #89818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D28 | 2 |
| C2×#66634 | 2 |
| C7×#946 | 2 |
| C2×C3×#1143 | 2 |
| #10620504 | 2 |
| #10620499 | 2 |
| (C2×D3)⋊(C7⋊C8) | 2 |
| #89818 | 3 |
| #5169 | 7 |