Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
340 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 107 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×C42×C7 | C2 | semidirect |
| 3. C2×#66627 | C2 | semidirect |
| 4. #10620644 | C2 | direct (N × H) |
| 11. #66728 | C4 | semidirect |
| 13. C2×D84 | C4 | semidirect |
| 15. C2×Dic42 | C4 | semidirect |
| 17. C3×C42×C7 | C22 | semidirect |
| 19. #66627 | C22 | semidirect |
| 22. C2×C42×C7 | D3 | semidirect |
| 40. D84 | C2×C4 | semidirect |
| 44. Dic42 | C2×C4 | semidirect |
| 57. C42×C7 | C2×D3 | semidirect |
| 62. C2×C3×C42 | D7 | semidirect |
| 109. C3×C42 | C2×D7 | semidirect |
| 115. C2×C3×C7 | #104 | semidirect |
| 120. C2×C42 | D21 | semidirect |
| 154. C3×C7 | C2×#104 | semidirect |
| 169. C42 | C2×D21 | semidirect |
| 172. C2×C7 | #805 | semidirect |
| 207. C7 | C2×#805 | semidirect |
| 210. C2×C3 | #6379 | semidirect |
| 225. C3 | C2×#6379 | semidirect |
| 229. C2 | #10620644 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66728 | 2 |
| C2×C3×C42×C7 | 2 |
| C2×#66627 | 2 |
| #10620644 | 2 |
| C2×#6379 | 3 |
| C2×#805 | 7 |