Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
516 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 516 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. C22×C7×Dic6 | C2 | semidirect |
| 3. C2×C3×#1136 | C2 | semidirect |
| 4. #10620883 | C2 | direct (N × H) |
| 5. C2×#66571 | C2 | semidirect |
| 6. C2×#66568 | C2 | semidirect |
| 19. C2×C7×Dic6 | C22 | semidirect |
| 20. C3×#1136 | C22 | semidirect |
| 22. #66571 | C22 | semidirect |
| 23. #66568 | C22 | semidirect |
| 29. C2×#1136 | D3 | semidirect |
| 64. #1136 | C2×D3 | semidirect |
| 67. C22×Dic6 | D7 | semidirect |
| 113. C2×Dic6 | C2×D7 | semidirect |
| 119. C2×C3×C7 | #137 | semidirect |
| 157. C3×C7 | C2×#137 | semidirect |
| 175. C2×C7 | #909 | semidirect |
| 207. C7 | C2×#909 | semidirect |
| 209. C2×C3 | #6505 | semidirect |
| 222. C3 | C2×#6505 | semidirect |
| 225. C2 | #10620883 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66728 | 2 |
| C22×C7×Dic6 | 2 |
| C2×C3×#1136 | 2 |
| #10620883 | 2 |
| C2×#66571 | 2 |
| C2×#66568 | 2 |
| C2×#6505 | 3 |
| C2×#909 | 7 |