Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
376 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 80 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. #10621407 | C2 | semidirect |
| 3. C2×#66567 | C2 | semidirect |
| 4. C3×C22⋊(C7⋊C8) | C2 | semidirect |
| 5. #10620502 | C2 | semidirect |
| 9. C2×Dic42 | C22 | semidirect |
| 14. C4⋊Dic21 | C22 | semidirect |
| 16. C2×C3×C7⋊C8 | C22 | semidirect |
| 22. C22⋊(C7⋊C8) | D3 | semidirect |
| 49. C2×C7⋊C8 | C2×D3 | semidirect |
| 57. C22×C3×C7 | SD16 | semidirect |
| 110. C22×C7 | #204 | semidirect |
| 131. C3×C7 | #450 | semidirect |
| 150. C22×C3 | #1142 | semidirect |
| 175. C7 | #4731 | semidirect |
| 187. C22 | #66567 | semidirect |
| 193. C3 | #89990 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D12 | 2 |
| #10621407 | 2 |
| C2×#66567 | 2 |
| C3×C22⋊(C7⋊C8) | 2 |
| #10620502 | 2 |
| #89990 | 3 |
| #4731 | 7 |