Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
304 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 86 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×C7×C22⋊Q8 | C2 | semidirect |
| 3. C2×C3×#1144 | C2 | semidirect |
| 4. C2×C3×#1143 | C2 | semidirect |
| 5. C3×C22⋊(C7⋊C8) | C2 | semidirect |
| 6. C3×#6384 | C2 | semidirect |
| 7. C3×#6383 | C2 | semidirect |
| 8. #89819 | C3 | direct (N × H) |
| 25. C7×C22⋊Q8 | C2×C3 | semidirect |
| 26. C2×#1144 | C2×C3 | semidirect |
| 27. C2×#1143 | C2×C3 | semidirect |
| 28. C22⋊(C7⋊C8) | C2×C3 | semidirect |
| 29. #6384 | C2×C3 | semidirect |
| 30. #6383 | C2×C3 | semidirect |
| 69. C3×C22⋊Q8 | D7 | semidirect |
| 129. C22⋊Q8 | C3×D7 | semidirect |
| 165. C3×C7 | #452 | semidirect |
| 218. C7 | C3×#452 | semidirect |
| 237. C3 | #89819 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1157 | 2 |
| C3×C7×C22⋊Q8 | 2 |
| C2×C3×#1144 | 2 |
| C2×C3×#1143 | 2 |
| C3×C22⋊(C7⋊C8) | 2 |
| C3×#6384 | 2 |
| C3×#6383 | 2 |
| #89819 | 3 |
| C3×#452 | 7 |