Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 110 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. C2×C3×C8×D7 | C2 | semidirect |
| 3. C3×#6455 | C2 | semidirect |
| 4. C3×C7×#102 | C2 | semidirect |
| 5. C3×#6406 | C2 | semidirect |
| 6. C3×#6390 | C2 | semidirect |
| 7. C3×#6384 | C2 | semidirect |
| 8. #89544 | C3 | direct (N × H) |
| 13. C3×#1159 | C4 | semidirect |
| 24. C2×C8×D7 | C2×C3 | semidirect |
| 25. #6455 | C2×C3 | semidirect |
| 26. C7×#102 | C2×C3 | semidirect |
| 27. #6406 | C2×C3 | semidirect |
| 28. #6390 | C2×C3 | semidirect |
| 29. #6384 | C2×C3 | semidirect |
| 52. #1159 | C3×C4 | semidirect |
| 68. C3×#102 | D7 | semidirect |
| 125. #102 | C3×D7 | semidirect |
| 156. C3×C7 | #416 | semidirect |
| 206. C7 | C3×#416 | semidirect |
| 225. C3 | #89544 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1159 | 2 |
| C2×C3×C8×D7 | 2 |
| C3×#6455 | 2 |
| C3×C7×#102 | 2 |
| C3×#6406 | 2 |
| C3×#6390 | 2 |
| C3×#6384 | 2 |
| #89544 | 3 |
| C3×#416 | 7 |