Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 3. #10620895 | C2 | semidirect |
| 4. C7×#818 | C2 | semidirect |
| 5. C3×#6389 | C2 | semidirect |
| 6. #10620510 | C2 | semidirect |
| 13. #66623 | C4 | semidirect |
| 25. #6389 | D3 | semidirect |
| 35. Dic42 | C2×C4 | semidirect |
| 41. C3×C7×C8 | C2×C4 | semidirect |
| 60. #818 | D7 | semidirect |
| 86. C7×C8 | C4×D3 | semidirect |
| 135. C3×C8 | C4×D7 | semidirect |
| 136. C3×C7 | #440 | semidirect |
| 177. C8 | D21⋊C4 | semidirect |
| 178. C7 | #4710 | semidirect |
| 194. C3 | #89661 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66623 | 2 |
| #10620980 | 2 |
| #10620895 | 2 |
| C7×#818 | 2 |
| C3×#6389 | 2 |
| #10620510 | 2 |
| #10620504 | 2 |
| #89661 | 3 |
| #4710 | 7 |