Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
260 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 86 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×#124 | C2 | semidirect |
| 2. C2×C3×#1144 | C2 | semidirect |
| 3. C2×C3×#1143 | C2 | semidirect |
| 4. C2×C3×#1142 | C2 | semidirect |
| 6. C3×#6438 | C2 | semidirect |
| 7. C3×C4×C7⋊C8 | C2 | semidirect |
| 8. #89831 | C3 | direct (N × H) |
| 22. C7×#124 | C2×C3 | semidirect |
| 23. C2×#1144 | C2×C3 | semidirect |
| 24. C2×#1143 | C2×C3 | semidirect |
| 25. C2×#1142 | C2×C3 | semidirect |
| 27. #6438 | C2×C3 | semidirect |
| 28. C4×C7⋊C8 | C2×C3 | semidirect |
| 64. C3×#124 | D7 | semidirect |
| 115. #124 | C3×D7 | semidirect |
| 143. C3×C7 | #495 | semidirect |
| 187. C7 | C3×#495 | semidirect |
| 202. C3 | #89831 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#124 | 2 |
| C2×C3×#1144 | 2 |
| C2×C3×#1143 | 2 |
| C2×C3×#1142 | 2 |
| C2×C3×#1141 | 2 |
| C3×#6438 | 2 |
| C3×C4×C7⋊C8 | 2 |
| #89831 | 3 |
| C3×#495 | 7 |