Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 6. #89862 | C3 | direct (N × H) |
| 52. C3×C4×C7 | Q16 | semidirect |
| 90. C4×C7 | C3×Q16 | semidirect |
| 106. C3×C7 | #462 | semidirect |
| 125. C3×C4 | #1144 | semidirect |
| 139. C7 | C3×#462 | semidirect |
| 148. C4 | C3×#1144 | semidirect |
| 151. C3 | #89862 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×C4⋊Q8 | 2 |
| C2×C3×#1144 | 2 |
| C3×C4×Dic14 | 2 |
| C3×#6409 | 2 |
| C3×C4⋊(C7⋊C8) | 2 |
| #89862 | 3 |
| C3×#462 | 7 |