Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
264 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 102 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. C4×C7×D12 | C2 | semidirect |
| 3. C3×C7×#97 | C2 | semidirect |
| 4. C7×#821 | C2 | semidirect |
| 5. C7×#817 | C2 | semidirect |
| 14. C7×D24 | C4 | semidirect |
| 19. C7×#97 | D3 | semidirect |
| 20. #4711 | C7 | direct (N × H) |
| 26. C7×D12 | C2×C4 | semidirect |
| 29. C3×C7×C8 | C2×C4 | semidirect |
| 39. C4×D12 | C2×C7 | semidirect |
| 40. C3×#97 | C2×C7 | semidirect |
| 41. #821 | C2×C7 | semidirect |
| 42. #817 | C2×C7 | semidirect |
| 60. C7×C8 | C4×D3 | semidirect |
| 68. D24 | C4×C7 | semidirect |
| 76. #97 | D3×C7 | semidirect |
| 90. D12 | C2×C4×C7 | semidirect |
| 93. C3×C8 | C2×C4×C7 | semidirect |
| 94. C3×C7 | #442 | semidirect |
| 122. C8 | C4×D3×C7 | semidirect |
| 123. C7 | #4711 | direct (N × H) |
| 135. C3 | C7×#442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×D24 | 2 |
| C4×C7×D12 | 2 |
| C3×C7×#97 | 2 |
| C7×#821 | 2 |
| C7×#817 | 2 |
| C7×#442 | 3 |
| #4711 | 7 |