Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
516 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 144 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×D7×Dic6 | C2 | semidirect |
| 3. C2×#66633 | C2 | semidirect |
| 4. C2×C7×#214 | C2 | semidirect |
| 5. #10621046 | C2 | direct (N × H) |
| 6. C2×#66570 | C2 | semidirect |
| 7. C2×#66569 | C2 | semidirect |
| 8. C2×#66557 | C2 | semidirect |
| 22. D7×Dic6 | C22 | semidirect |
| 23. #66633 | C22 | semidirect |
| 25. C7×#214 | C22 | semidirect |
| 27. #66570 | C22 | semidirect |
| 28. #66569 | C22 | semidirect |
| 29. #66557 | C22 | semidirect |
| 88. C2×#214 | D7 | semidirect |
| 141. #214 | C2×D7 | semidirect |
| 146. C2×C3×C7 | #137 | semidirect |
| 191. C3×C7 | C2×#137 | semidirect |
| 213. C2×C7 | #951 | semidirect |
| 250. C7 | C2×#951 | semidirect |
| 253. C2×C3 | #6478 | semidirect |
| 266. C3 | C2×#6478 | semidirect |
| 269. C2 | #10621046 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1159 | 2 |
| C2×D7×Dic6 | 2 |
| C2×#66633 | 2 |
| C2×C7×#214 | 2 |
| #10621046 | 2 |
| C2×#66570 | 2 |
| C2×#66569 | 2 |
| C2×#66557 | 2 |
| C2×#6478 | 3 |
| C2×#951 | 7 |