Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
372 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 92 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. D7×#208 | C2 | semidirect |
| 3. #10620672 | C2 | semidirect |
| 4. C7×#833 | C2 | semidirect |
| 5. #10620493 | C2 | semidirect |
| 14. #66627 | C22 | semidirect |
| 15. C7×#208 | C22 | semidirect |
| 54. #833 | D7 | direct (N × H) |
| 92. #208 | C2×D7 | semidirect |
| 99. C3×D7 | #100 | semidirect |
| 132. C3×C7 | C2×#100 | semidirect |
| 149. D7 | #833 | direct (N × H) |
| 177. C7 | C2×#833 | 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×C3×D4×D7 | 2 |
| D7×#208 | 2 |
| #10620672 | 2 |
| C7×#833 | 2 |
| #10620493 | 2 |
| D7×#100 | 3 |
| C2×#833 | 7 |