Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×C3⋊(C7⋊C8) | C2 | semidirect |
| 3. #10620669 | C2 | semidirect |
| 4. C4⋊(C3⋊(C7⋊C8)) | C2 | semidirect |
| 5. C4×C3⋊(C7⋊C8) | C2 | semidirect |
| 23. C3×C7×D4 | C8 | semidirect |
| 32. C3⋊(C7⋊C8) | D4 | direct (N × H) |
| 49. C22×C3×C7 | C2×C8 | semidirect |
| 53. C3×C4×C7 | C2×C8 | semidirect |
| 58. C7×D4 | C3⋊C8 | semidirect |
| 88. C22×C7 | C2×C3⋊C8 | semidirect |
| 92. C4×C7 | C2×C3⋊C8 | semidirect |
| 96. C3×D4 | C7⋊C8 | semidirect |
| 106. C3×C7 | C8×D4 | semidirect |
| 122. C22×C3 | C2×C7⋊C8 | semidirect |
| 126. C3×C4 | C2×C7⋊C8 | semidirect |
| 130. D4 | C3⋊(C7⋊C8) | direct (N × H) |
| 140. C7 | D4×C3⋊C8 | semidirect |
| 147. C22 | C2×C3⋊(C7⋊C8) | semidirect |
| 151. C4 | C2×C3⋊(C7⋊C8) | semidirect |
| 154. C3 | D4×C7⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×D4 | 2 |
| C22×C3⋊(C7⋊C8) | 2 |
| #10620669 | 2 |
| C4⋊(C3⋊(C7⋊C8)) | 2 |
| C4×C3⋊(C7⋊C8) | 2 |
| D4×C7⋊C8 | 3 |
| D4×C3⋊C8 | 7 |