Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
300 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 75 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. M16×D21 | C2 | semidirect |
| 3. C3×C7×#101 | C2 | semidirect |
| 4. #10620675 | C2 | semidirect |
| 5. #10620662 | C2 | semidirect |
| 20. C7×#101 | D3 | semidirect |
| 51. C3×#101 | D7 | semidirect |
| 96. #101 | D21 | semidirect |
| 121. C3×C7 | #413 | semidirect |
| 160. C7 | #4751 | semidirect |
| 174. C3 | #89523 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66732 | 2 |
| M16×D21 | 2 |
| C3×C7×#101 | 2 |
| #10620675 | 2 |
| #10620662 | 2 |
| #89523 | 3 |
| #4751 | 7 |