Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
292 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 292 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 |
|---|---|---|
| 1. C3×#6551 | C2 | semidirect |
| 2. C3×C7×#124 | C2 | semidirect |
| 3. C3×#6495 | C2 | semidirect |
| 4. C3×#6410 | C2 | semidirect |
| 5. C3×#6379 | C2 | semidirect |
| 6. #89834 | C3 | direct (N × H) |
| 18. #6551 | C2×C3 | semidirect |
| 19. C7×#124 | C2×C3 | semidirect |
| 20. #6495 | C2×C3 | semidirect |
| 21. #6410 | C2×C3 | semidirect |
| 22. #6379 | C2×C3 | semidirect |
| 51. C3×#124 | D7 | semidirect |
| 94. #124 | C3×D7 | semidirect |
| 119. C3×C7 | #454 | semidirect |
| 157. C7 | C3×#454 | semidirect |
| 170. C3 | #89834 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6551 | 2 |
| C3×C7×#124 | 2 |
| C3×#6495 | 2 |
| C3×#6410 | 2 |
| C3×#6379 | 2 |
| #89834 | 3 |
| C3×#454 | 7 |