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×C3×Dic14 | C2 | semidirect |
| 3. C2×#66627 | C2 | semidirect |
| 4. C2×#66569 | C2 | semidirect |
| 5. #10620871 | C2 | direct (N × H) |
| 6. C2×#66564 | C2 | semidirect |
| 19. C2×C3×Dic14 | C22 | semidirect |
| 20. #66627 | C22 | semidirect |
| 22. #66569 | C22 | semidirect |
| 23. #66564 | C22 | semidirect |
| 25. C22×Dic14 | D3 | semidirect |
| 61. C2×Dic14 | C2×D3 | semidirect |
| 119. C2×C3×C7 | #137 | semidirect |
| 157. C3×C7 | C2×#137 | semidirect |
| 176. C2×C7 | #942 | semidirect |
| 207. C7 | C2×#942 | semidirect |
| 209. C2×C3 | #6514 | semidirect |
| 222. C3 | C2×#6514 | semidirect |
| 225. C2 | #10620871 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#235 | 2 |
| C22×C3×Dic14 | 2 |
| C2×#66627 | 2 |
| C2×#66569 | 2 |
| #10620871 | 2 |
| C2×#66564 | 2 |
| C2×#6514 | 3 |
| C2×#942 | 7 |