Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 110 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. C3×C4×D28 | C2 | semidirect |
| 3. C3×C4×C7×C8 | C2 | semidirect |
| 4. C3×#6395 | C2 | semidirect |
| 5. C3×#6392 | C2 | semidirect |
| 6. C4×D56 | C3 | direct (N × H) |
| 14. C3×D56 | C4 | direct (N × H) |
| 16. C4×D28 | C2×C3 | semidirect |
| 17. C4×C7×C8 | C2×C3 | semidirect |
| 18. #6395 | C2×C3 | semidirect |
| 19. #6392 | C2×C3 | semidirect |
| 27. C3×D28 | C2×C4 | semidirect |
| 30. C3×C7×C8 | C2×C4 | semidirect |
| 38. D56 | C3×C4 | direct (N × H) |
| 43. C3×C4×C8 | D7 | semidirect |
| 49. C3×C4×C7 | D8 | semidirect |
| 60. D28 | C2×C3×C4 | semidirect |
| 63. C7×C8 | C2×C3×C4 | semidirect |
| 80. C4×C8 | C3×D7 | semidirect |
| 86. C4×C7 | C3×D8 | semidirect |
| 99. C3×C8 | C4×D7 | semidirect |
| 100. C3×C7 | C4×D8 | semidirect |
| 119. C3×C4 | D56 | direct (N × H) |
| 131. C8 | C3×C4×D7 | semidirect |
| 132. C7 | C3×C4×D8 | semidirect |
| 143. C4 | C3×D56 | direct (N × H) |
| 146. C3 | C4×D56 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D56 | 2 |
| C3×C4×D28 | 2 |
| C3×C4×C7×C8 | 2 |
| C3×#6395 | 2 |
| C3×#6392 | 2 |
| C4×D56 | 3 |
| C3×C4×D8 | 7 |