Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
208 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 94 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×#6464 | C2 | semidirect |
| 3. C3×C7×#97 | C2 | semidirect |
| 4. C3×#6393 | C2 | semidirect |
| 5. C3×#6379 | C2 | semidirect |
| 6. #89489 | C3 | direct (N × H) |
| 12. C3×Dic28 | C4 | semidirect |
| 13. C3×D56 | C4 | semidirect |
| 14. C3×#1132 | C4 | semidirect |
| 18. #6464 | C2×C3 | semidirect |
| 19. C7×#97 | C2×C3 | semidirect |
| 20. #6393 | C2×C3 | semidirect |
| 21. #6379 | C2×C3 | semidirect |
| 38. Dic28 | C3×C4 | semidirect |
| 39. D56 | C3×C4 | semidirect |
| 40. #1132 | C3×C4 | semidirect |
| 47. C3×#97 | D7 | semidirect |
| 82. #97 | C3×D7 | semidirect |
| 99. C3×C7 | #444 | semidirect |
| 129. C7 | C3×#444 | semidirect |
| 139. C3 | #89489 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6467 | 2 |
| C3×#6464 | 2 |
| C3×C7×#97 | 2 |
| C3×#6393 | 2 |
| C3×#6379 | 2 |
| #89489 | 3 |
| C3×#444 | 7 |