Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
264 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 83 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. C3×C4×C7×D4 | C2 | semidirect |
| 3. C4×D84 | C2 | semidirect |
| 4. #10620671 | C2 | semidirect |
| 5. #10620648 | C2 | semidirect |
| 6. #10620647 | C2 | semidirect |
| 7. #10620642 | C2 | semidirect |
| 16. #66632 | C4 | semidirect |
| 21. C4×C7×D4 | D3 | semidirect |
| 32. C3×C7×D4 | C2×C4 | semidirect |
| 40. D84 | C2×C4 | semidirect |
| 43. C3⋊(C7⋊C8) | C2×C4 | semidirect |
| 56. C3×C4×D4 | D7 | semidirect |
| 80. C7×D4 | C4×D3 | semidirect |
| 111. C4×D4 | D21 | semidirect |
| 132. C3×D4 | C4×D7 | semidirect |
| 144. C3×C7 | #442 | semidirect |
| 180. D4 | C4×D21 | semidirect |
| 190. C7 | #5014 | semidirect |
| 209. C3 | #89786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×D4 | 2 |
| C2×#66632 | 2 |
| C4×D84 | 2 |
| #10620671 | 2 |
| #10620648 | 2 |
| #10620647 | 2 |
| #10620642 | 2 |
| #89786 | 3 |
| #5014 | 7 |