Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
260 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 82 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×C7×#121 | C2 | semidirect |
| 2. C2×C3×#1141 | C2 | semidirect |
| 3. C3×#6493 | C2 | semidirect |
| 4. C2×C3×#1136 | C2 | semidirect |
| 5. C3×#6406 | C2 | semidirect |
| 6. C3×#6383 | C2 | semidirect |
| 7. C3×#6382 | C2 | semidirect |
| 8. #89811 | C3 | direct (N × H) |
| 22. C7×#121 | C2×C3 | semidirect |
| 23. C2×#1141 | C2×C3 | semidirect |
| 24. #6493 | C2×C3 | semidirect |
| 25. C2×#1136 | C2×C3 | semidirect |
| 26. #6406 | C2×C3 | semidirect |
| 27. #6383 | C2×C3 | semidirect |
| 28. #6382 | C2×C3 | semidirect |
| 46. C3×C7⋊C8 | D4 | semidirect |
| 63. C3×#121 | D7 | semidirect |
| 99. C7⋊C8 | C3×D4 | semidirect |
| 122. #121 | C3×D7 | semidirect |
| 158. C3×C7 | #469 | semidirect |
| 210. C7 | C3×#469 | semidirect |
| 232. C3 | #89811 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#121 | 2 |
| C2×C3×#1141 | 2 |
| C3×#6493 | 2 |
| C2×C3×#1136 | 2 |
| C3×#6406 | 2 |
| C3×#6383 | 2 |
| C3×#6382 | 2 |
| #89811 | 3 |
| C3×#469 | 7 |