Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 102 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×#127 | C2 | semidirect |
| 2. C2×C3×#1141 | C2 | semidirect |
| 3. C3×#6437 | C2 | semidirect |
| 4. C3×C4×C7⋊C8 | C2 | semidirect |
| 5. #89845 | C3 | direct (N × H) |
| 13. C7×#127 | C2×C3 | semidirect |
| 14. C2×#1141 | C2×C3 | semidirect |
| 15. #6437 | C2×C3 | semidirect |
| 16. C4×C7⋊C8 | C2×C3 | semidirect |
| 26. C3×C7⋊C8 | D4 | semidirect |
| 36. C3×#127 | D7 | semidirect |
| 43. C3×C4×C7 | D8 | semidirect |
| 54. C7⋊C8 | C3×D4 | semidirect |
| 68. #127 | C3×D7 | semidirect |
| 75. C4×C7 | C3×D8 | semidirect |
| 86. C3×C7 | #493 | semidirect |
| 103. C3×C4 | #1141 | semidirect |
| 114. C7 | C3×#493 | semidirect |
| 124. C4 | C3×#1141 | semidirect |
| 126. C3 | #89845 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#127 | 2 |
| C2×C3×#1141 | 2 |
| C3×#6437 | 2 |
| C3×C4×C7⋊C8 | 2 |
| #89845 | 3 |
| C3×#493 | 7 |