Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
420 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 92 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. D7×#217 | C2 | semidirect |
| 3. #10620673 | C2 | semidirect |
| 4. C7×#834 | C2 | semidirect |
| 5. #10620530 | C2 | semidirect |
| 7. C23×C3×D7 | C4 | semidirect |
| 10. C2×C3×C22⋊D7 | C4 | semidirect |
| 14. C2×C3×D28 | C4 | semidirect |
| 15. C2×C3×C4×D7 | C4 | semidirect |
| 17. #66636 | C22 | semidirect |
| 18. C7×#217 | C22 | semidirect |
| 26. C23×C3×C7 | C2×C4 | semidirect |
| 34. C22×C3×D7 | C2×C4 | semidirect |
| 38. C2×C3×C4×C7 | C2×C4 | semidirect |
| 43. C2×C3×Dic7 | C2×C4 | semidirect |
| 48. C23×D7 | Dic3 | semidirect |
| 51. C2×C22⋊D7 | Dic3 | semidirect |
| 55. C2×D28 | Dic3 | semidirect |
| 57. C2×C4×D7 | Dic3 | semidirect |
| 65. #834 | D7 | direct (N × H) |
| 87. C23×C7 | C2×Dic3 | semidirect |
| 95. C22×D7 | C2×Dic3 | semidirect |
| 100. C2×C4×C7 | C2×Dic3 | semidirect |
| 104. C2×Dic7 | C2×Dic3 | semidirect |
| 121. #217 | C2×D7 | semidirect |
| 129. C3×D7 | #99 | semidirect |
| 164. C23×C3 | C4×D7 | semidirect |
| 173. C2×C3×C4 | C4×D7 | semidirect |
| 177. C3×C7 | C2×#99 | semidirect |
| 198. D7 | #834 | direct (N × H) |
| 228. C23 | Dic3×D7 | semidirect |
| 240. C2×C4 | Dic3×D7 | semidirect |
| 241. C7 | C2×#834 | semidirect |
| 270. C3 | D7×#99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×D7 | 2 |
| D7×#217 | 2 |
| #10620673 | 2 |
| C7×#834 | 2 |
| #10620530 | 2 |
| D7×#99 | 3 |
| C2×#834 | 7 |