Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
580 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 224 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 |
|---|---|---|
| 5. #10620938 | C2 | direct (N × H) |
| 32. C2×C3×Dic7 | Q8 | semidirect |
| 54. C3×Dic7 | C2×Q8 | semidirect |
| 65. C2×Dic7 | Dic6 | semidirect |
| 78. C2×C3×C7 | C4⋊Q8 | semidirect |
| 92. Dic7 | C2×Dic6 | semidirect |
| 104. C3×C7 | C2×C4⋊Q8 | semidirect |
| 115. C2×C7 | #869 | semidirect |
| 136. C7 | C2×#869 | semidirect |
| 137. C2×C3 | #6507 | semidirect |
| 147. C3 | C2×#6507 | semidirect |
| 148. C2 | #10620938 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic42 | 2 |
| C22×C7×Dic6 | 2 |
| C2×C3×C4×Dic7 | 2 |
| C2×Dic7⋊Dic3 | 2 |
| #10620938 | 2 |
| C2×#6507 | 3 |
| C2×#869 | 7 |