Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
492 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 160 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×C4×C7×Dic3 | C2 | semidirect |
| 3. C2×C3×Dic7⋊C4 | C2 | semidirect |
| 4. C2×#66577 | C2 | semidirect |
| 5. C2×Dic7⋊Dic3 | C2 | semidirect |
| 8. #10620942 | C2 | direct (N × H) |
| 18. C4×C7×Dic3 | C22 | semidirect |
| 19. C3×Dic7⋊C4 | C22 | semidirect |
| 20. #66577 | C22 | semidirect |
| 21. Dic7⋊Dic3 | C22 | semidirect |
| 30. C2×Dic7⋊C4 | D3 | semidirect |
| 63. Dic7⋊C4 | C2×D3 | semidirect |
| 70. C2×C4×Dic3 | D7 | semidirect |
| 117. C4×Dic3 | C2×D7 | semidirect |
| 118. C2×C3×C7 | #126 | semidirect |
| 162. C3×C7 | C2×#126 | semidirect |
| 177. C2×C7 | #898 | semidirect |
| 213. C7 | C2×#898 | semidirect |
| 214. C2×C3 | #6439 | semidirect |
| 233. C3 | C2×#6439 | semidirect |
| 235. C2 | #10620942 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66631 | 2 |
| C2×C4×C7×Dic3 | 2 |
| C2×C3×Dic7⋊C4 | 2 |
| C2×#66577 | 2 |
| C2×Dic7⋊Dic3 | 2 |
| C2×#66575 | 2 |
| #10620942 | 2 |
| C2×#6439 | 3 |
| C2×#898 | 7 |