Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 86 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. D3×C7×C4⋊C4 | C2 | semidirect |
| 3. C2×#66558 | C2 | semidirect |
| 4. #10620648 | C2 | semidirect |
| 5. C3×#6384 | C2 | semidirect |
| 6. #10620505 | C2 | semidirect |
| 7. #10620504 | C2 | semidirect |
| 16. #66673 | C4 | semidirect |
| 27. #6384 | D3 | semidirect |
| 36. D84 | C2×C4 | semidirect |
| 44. C3×Dic14 | C2×C4 | semidirect |
| 65. D3×C4⋊C4 | D7 | semidirect |
| 99. Dic14 | C4×D3 | semidirect |
| 159. C3×C7 | #417 | semidirect |
| 210. C7 | #4803 | semidirect |
| 229. C3 | #89738 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66673 | 2 |
| D3×C7×C4⋊C4 | 2 |
| C2×#66558 | 2 |
| #10620648 | 2 |
| C3×#6384 | 2 |
| #10620505 | 2 |
| #10620504 | 2 |
| #89738 | 3 |
| #4803 | 7 |