Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
252 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 120 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. Dic7⋊(C3⋊C8) | C2 | semidirect |
| 50. C3×Dic7 | M16 | semidirect |
| 85. Dic7 | #208 | semidirect |
| 96. C3×C7 | #423 | semidirect |
| 127. C7 | #4924 | semidirect |
| 139. C3 | #89890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66627 | 2 |
| C2×C7×#208 | 2 |
| C2×C3×C4×Dic7 | 2 |
| Dic7⋊(C3⋊C8) | 2 |
| #89890 | 3 |
| #4924 | 7 |