Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 1. Q8×Dic21 | C2 | semidirect |
| 4. C3×#6409 | C2 | semidirect |
| 5. #10620525 | C2 | semidirect |
| 7. #10620489 | C2 | semidirect |
| 16. C7×#215 | C4 | semidirect |
| 24. #6409 | D3 | semidirect |
| 31. C3×C7×Q8 | C2×C4 | semidirect |
| 42. C7×C3⋊C8 | C2×C4 | semidirect |
| 76. C7×Q8 | C4×D3 | semidirect |
| 93. #215 | Dic7 | semidirect |
| 124. C3×Q8 | C2×Dic7 | semidirect |
| 135. C3⋊C8 | C2×Dic7 | semidirect |
| 136. C3×C7 | #440 | semidirect |
| 166. Q8 | D3×Dic7 | semidirect |
| 178. C7 | #4817 | semidirect |
| 194. C3 | #89936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic21 | 2 |
| C2×C7×#215 | 2 |
| #10620997 | 2 |
| C3×#6409 | 2 |
| #10620525 | 2 |
| #10620502 | 2 |
| #10620489 | 2 |
| #89936 | 3 |
| #4817 | 7 |