Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
276 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. C3×C7×C4⋊C8 | C2 | semidirect |
| 4. #10620653 | C2 | semidirect |
| 5. C4⋊(C3⋊(C7⋊C8)) | C2 | semidirect |
| 19. C7×C4⋊C8 | D3 | semidirect |
| 31. C4×D21 | C8 | semidirect |
| 48. C3×C4⋊C8 | D7 | semidirect |
| 56. C3×C4×C7 | C2×C8 | semidirect |
| 61. Dic21 | C2×C8 | semidirect |
| 89. D21 | C4⋊C8 | direct (N × H) |
| 94. C4⋊C8 | D21 | direct (N × H) |
| 100. C4×C7 | D3×C8 | semidirect |
| 119. C3×C7 | C2×C4⋊C8 | semidirect |
| 139. C3×C4 | C8×D7 | semidirect |
| 158. C7 | D3×C4⋊C8 | semidirect |
| 171. C4 | C8×D21 | semidirect |
| 174. C3 | D7×C4⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D21 | 2 |
| C42×D21 | 2 |
| C3×C7×C4⋊C8 | 2 |
| #10620653 | 2 |
| C4⋊(C3⋊(C7⋊C8)) | 2 |
| D7×C4⋊C8 | 3 |
| D3×C4⋊C8 | 7 |