Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
660 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 272 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×Dic21 | C2 | semidirect |
| 3. C2×C4×C7×Dic3 | C2 | semidirect |
| 4. C2×Dic7⋊Dic3 | C2 | semidirect |
| 6. #10620919 | C2 | direct (N × H) |
| 13. C2×C3×C4×D7 | C4 | semidirect |
| 15. C4×Dic21 | C22 | semidirect |
| 16. C4×C7×Dic3 | C22 | semidirect |
| 17. Dic7⋊Dic3 | C22 | semidirect |
| 38. C3×C4×D7 | C2×C4 | semidirect |
| 44. C2×C4×D7 | Dic3 | semidirect |
| 55. C2×C4×Dic3 | D7 | semidirect |
| 79. C4×D7 | C2×Dic3 | semidirect |
| 90. C4×Dic3 | C2×D7 | semidirect |
| 91. C2×C3×C7 | #117 | semidirect |
| 124. C3×C7 | C2×#117 | semidirect |
| 136. C2×C7 | #926 | semidirect |
| 163. C7 | C2×#926 | semidirect |
| 165. C2×C3 | #6435 | semidirect |
| 178. C3 | C2×#6435 | semidirect |
| 180. C2 | #10620919 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×D7 | 2 |
| C2×C4×Dic21 | 2 |
| C2×C4×C7×Dic3 | 2 |
| C2×Dic7⋊Dic3 | 2 |
| C2×(C2×D7)⋊Dic3 | 2 |
| #10620919 | 2 |
| C2×#6435 | 3 |
| C2×#926 | 7 |