Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
304 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 78 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×#124 | C2 | semidirect |
| 3. C3×#6505 | C2 | semidirect |
| 4. C3×#6407 | C2 | semidirect |
| 5. C3×#6379 | C2 | semidirect |
| 6. #89833 | C3 | direct (N × H) |
| 7. C2×C3×C7×Q8 | C22 | semidirect |
| 14. C3×C42×C7 | C22 | semidirect |
| 17. C3×#1136 | C22 | semidirect |
| 19. C7×#124 | C2×C3 | semidirect |
| 20. #6505 | C2×C3 | semidirect |
| 21. #6407 | C2×C3 | semidirect |
| 22. #6379 | C2×C3 | semidirect |
| 38. C2×C7×Q8 | C22×C3 | semidirect |
| 45. C42×C7 | C22×C3 | semidirect |
| 48. #1136 | C22×C3 | semidirect |
| 51. C3×#124 | D7 | semidirect |
| 80. C2×C3×Q8 | C2×D7 | semidirect |
| 88. C3×C42 | C2×D7 | semidirect |
| 95. #124 | C3×D7 | semidirect |
| 121. C3×C7 | #455 | semidirect |
| 124. C2×Q8 | C2×C3×D7 | semidirect |
| 132. C42 | C2×C3×D7 | semidirect |
| 160. C7 | C3×#455 | semidirect |
| 174. C3 | #89833 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6548 | 2 |
| C3×C7×#124 | 2 |
| C3×#6505 | 2 |
| C3×#6407 | 2 |
| C3×#6379 | 2 |
| #89833 | 3 |
| C3×#455 | 7 |