Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
288 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 288 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×#127 | C2 | semidirect |
| 2. C2×C3×#1142 | C2 | semidirect |
| 3. C2×C3×#1141 | C2 | semidirect |
| 4. C3×#6438 | C2 | semidirect |
| 5. C3×#6377 | C2 | semidirect |
| 6. #89846 | C3 | direct (N × H) |
| 16. C7×#127 | C2×C3 | semidirect |
| 17. C2×#1142 | C2×C3 | semidirect |
| 18. C2×#1141 | C2×C3 | semidirect |
| 19. #6438 | C2×C3 | semidirect |
| 20. #6377 | C2×C3 | semidirect |
| 32. C3×C7⋊C8 | D4 | semidirect |
| 44. C3×#127 | D7 | semidirect |
| 66. C7⋊C8 | C3×D4 | semidirect |
| 82. #127 | C3×D7 | semidirect |
| 104. C3×C7 | #496 | semidirect |
| 137. C7 | C3×#496 | semidirect |
| 150. C3 | #89846 | 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×#1142 | 2 |
| C2×C3×#1141 | 2 |
| C3×#6438 | 2 |
| C3×#6377 | 2 |
| #89846 | 3 |
| C3×#496 | 7 |