Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 1. C2×#66673 | C2 | semidirect |
| 2. C2×#66632 | C2 | semidirect |
| 3. C7×#938 | C2 | semidirect |
| 4. C2×C3×#1142 | C2 | semidirect |
| 5. #10620505 | C2 | semidirect |
| 6. #10620504 | C2 | semidirect |
| 7. (C2×D3)⋊(C7⋊C8) | C2 | semidirect |
| 26. C2×#1142 | D3 | semidirect |
| 39. D84 | D4 | semidirect |
| 47. C3×Dic14 | D4 | semidirect |
| 69. #938 | D7 | semidirect |
| 107. Dic14 | #67 | semidirect |
| 173. C3×C7 | #449 | semidirect |
| 230. C7 | #5172 | semidirect |
| 252. C3 | #89809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66673 | 2 |
| C2×#66632 | 2 |
| C7×#938 | 2 |
| C2×C3×#1142 | 2 |
| #10620505 | 2 |
| #10620504 | 2 |
| (C2×D3)⋊(C7⋊C8) | 2 |
| #89809 | 3 |
| #5172 | 7 |