Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
164 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 52 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. #10620668 | C2 | semidirect |
| 4. C3×#6403 | C2 | semidirect |
| 5. #10620483 | C2 | semidirect |
| 6. #10620481 | C2 | semidirect |
| 25. #6403 | D3 | direct (N × H) |
| 88. D3×C7 | Q32 | semidirect |
| 114. C3×C7 | C2×Q32 | semidirect |
| 146. C7 | D3×Q32 | semidirect |
| 148. D3 | #6403 | direct (N × H) |
| 156. C3 | C2×#6403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C7×Q16 | 2 |
| D3×Dic28 | 2 |
| #10620668 | 2 |
| C3×#6403 | 2 |
| #10620483 | 2 |
| #10620481 | 2 |
| D3×C7⋊C16 | 2 |
| C2×#6403 | 3 |
| D3×Q32 | 7 |