Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
300 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 88 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. D3×#1136 | C2 | semidirect |
| 3. #10620675 | C2 | semidirect |
| 4. C3×#6410 | C2 | semidirect |
| 5. #10620494 | C2 | semidirect |
| 21. #6410 | D3 | semidirect |
| 121. C3×C7 | #413 | semidirect |
| 160. C7 | #4751 | semidirect |
| 174. C3 | #90009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#239 | 2 |
| D3×#1136 | 2 |
| #10620675 | 2 |
| C3×#6410 | 2 |
| #10620494 | 2 |
| #90009 | 3 |
| #4751 | 7 |