Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
220 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 4. #89318 | C3 | direct (N × H) |
| 8. C3×C42×C7 | C4 | semidirect |
| 10. C3×C4⋊Dic7 | C4 | semidirect |
| 13. C3×#1136 | C4 | semidirect |
| 33. C42×C7 | C3×C4 | semidirect |
| 35. C4⋊Dic7 | C3×C4 | semidirect |
| 38. #1136 | C3×C4 | semidirect |
| 74. C3×C42 | Dic7 | semidirect |
| 103. C3×C7 | #339 | semidirect |
| 113. C42 | C3×Dic7 | semidirect |
| 139. C7 | C3×#339 | semidirect |
| 154. C3 | #89318 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C42×C7 | 2 |
| C3×#6489 | 2 |
| C2×C3×#1136 | 2 |
| #89318 | 3 |
| C3×#339 | 7 |