Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
112 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 50 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×C7×C16 | C2 | semidirect |
| 3. C7×#819 | C2 | semidirect |
| 13. C2×C7×C16 | D3 | semidirect |
| 15. #4510 | C7 | direct (N × H) |
| 32. C2×C3×C16 | C2×C7 | semidirect |
| 33. #819 | C2×C7 | semidirect |
| 59. C2×C16 | D3×C7 | semidirect |
| 74. C3×C7 | #359 | semidirect |
| 98. C7 | #4510 | direct (N × H) |
| 107. C3 | C7×#359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#904 | 2 |
| C2×C3×C7×C16 | 2 |
| C7×#819 | 2 |
| C7×#359 | 3 |
| #4510 | 7 |