Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
308 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 118 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. C3×C7×#117 | C2 | semidirect |
| 3. C2×C3×#1136 | C2 | semidirect |
| 4. C3×#6379 | C2 | semidirect |
| 5. #89777 | C3 | direct (N × H) |
| 10. C3×#1157 | C4 | semidirect |
| 12. C2×C3×D28 | C4 | semidirect |
| 14. C2×C3×Dic14 | C4 | semidirect |
| 17. C3×C42×C7 | C22 | semidirect |
| 19. C3×#1136 | C22 | semidirect |
| 22. C7×#117 | C2×C3 | semidirect |
| 23. C2×#1136 | C2×C3 | semidirect |
| 24. #6379 | C2×C3 | semidirect |
| 49. #1157 | C3×C4 | semidirect |
| 51. C2×D28 | C3×C4 | semidirect |
| 53. C2×Dic14 | C3×C4 | semidirect |
| 56. C42×C7 | C22×C3 | semidirect |
| 58. #1136 | C22×C3 | semidirect |
| 62. C3×#117 | D7 | semidirect |
| 110. C3×C42 | C2×D7 | semidirect |
| 118. #117 | C3×D7 | semidirect |
| 151. C3×C7 | #421 | semidirect |
| 166. C42 | C2×C3×D7 | semidirect |
| 203. C7 | C3×#421 | semidirect |
| 221. C3 | #89777 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1157 | 2 |
| C3×C7×#117 | 2 |
| C2×C3×#1136 | 2 |
| C3×#6379 | 2 |
| #89777 | 3 |
| C3×#421 | 7 |