Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
580 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 286 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. C3×#6507 | C2 | direct (N × H) |
| 6. C2×#6507 | C3 | direct (N × H) |
| 19. #6507 | C2×C3 | direct (N × H) |
| 30. C2×C3×Dic7 | Q8 | semidirect |
| 55. C3×Dic7 | C2×Q8 | semidirect |
| 64. C2×Dic7 | C3×Q8 | semidirect |
| 78. C2×C3×C7 | C4⋊Q8 | semidirect |
| 92. Dic7 | C2×C3×Q8 | semidirect |
| 104. C3×C7 | C2×C4⋊Q8 | semidirect |
| 115. C2×C7 | C3×C4⋊Q8 | semidirect |
| 136. C7 | C2×C3×C4⋊Q8 | semidirect |
| 137. C2×C3 | #6507 | direct (N × H) |
| 147. C3 | C2×#6507 | direct (N × H) |
| 148. C2 | C3×#6507 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×Q8 | 2 |
| C22×C3×Dic14 | 2 |
| C3×#6507 | 2 |
| C2×C3×Dic7⋊C4 | 2 |
| C2×C3×C4×Dic7 | 2 |
| C2×#6507 | 3 |
| C2×C3×C4⋊Q8 | 7 |