Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
256 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 90 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×C7×#214 | C2 | semidirect |
| 3. C4×C7×Dic6 | C2 | semidirect |
| 4. C7×#832 | C2 | semidirect |
| 5. C7×C4⋊(C3⋊C8) | C2 | semidirect |
| 22. #5075 | C7 | direct (N × H) |
| 34. C7×Dic6 | D4 | semidirect |
| 47. C2×#214 | C2×C7 | semidirect |
| 48. C4×Dic6 | C2×C7 | semidirect |
| 49. #832 | C2×C7 | semidirect |
| 50. C4⋊(C3⋊C8) | C2×C7 | semidirect |
| 56. C3×C4×C7 | SD16 | semidirect |
| 101. C4×C7 | #214 | semidirect |
| 115. Dic6 | C7×D4 | semidirect |
| 117. C3×C7 | #460 | semidirect |
| 137. C3×C4 | C7×SD16 | semidirect |
| 155. C7 | #5075 | direct (N × H) |
| 167. C4 | C7×#214 | semidirect |
| 170. C3 | C7×#460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#127 | 2 |
| C2×C7×#214 | 2 |
| C4×C7×Dic6 | 2 |
| C7×#832 | 2 |
| C7×C4⋊(C3⋊C8) | 2 |
| C7×#460 | 3 |
| #5075 | 7 |