Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
192 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 94 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. #89792 | C3 | direct (N × H) |
| 23. C3×C7×Q8 | Q8 | semidirect |
| 56. C7×Q8 | C3×Q8 | semidirect |
| 92. C3×Q8 | Dic14 | semidirect |
| 100. C3×C7 | #475 | semidirect |
| 123. Q8 | C3×Dic14 | semidirect |
| 131. C7 | C3×#475 | semidirect |
| 143. C3 | #89792 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×Q8 | 2 |
| C3×#6432 | 2 |
| C3×#6409 | 2 |
| C3×#6382 | 2 |
| C3×C4⋊(C7⋊C8) | 2 |
| #89792 | 3 |
| C3×#475 | 7 |