Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
372 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 77 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×#100 | C2 | semidirect |
| 4. #10620672 | C2 | semidirect |
| 5. #10620662 | C2 | semidirect |
| 14. C3×C7×M16 | C22 | semidirect |
| 15. #66627 | C22 | semidirect |
| 20. C7×#100 | D3 | semidirect |
| 46. C7×M16 | C2×D3 | semidirect |
| 52. C3×#100 | D7 | semidirect |
| 90. C3×M16 | C2×D7 | semidirect |
| 99. D21 | #100 | direct (N × H) |
| 104. #100 | D21 | direct (N × H) |
| 132. C3×C7 | C2×#100 | semidirect |
| 142. M16 | C2×D21 | semidirect |
| 177. C7 | D3×#100 | semidirect |
| 196. C3 | D7×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D21 | 2 |
| M16×D21 | 2 |
| C3×C7×#100 | 2 |
| #10620672 | 2 |
| #10620662 | 2 |
| D7×#100 | 3 |
| D3×#100 | 7 |