Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
132 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×C3×C7×C16 | C2 | semidirect |
| 3. C2×C3⋊(C7⋊C16) | C2 | semidirect |
| 13. C2×C7×C16 | D3 | semidirect |
| 32. C2×C3×C16 | D7 | semidirect |
| 37. C2×D21 | C16 | semidirect |
| 63. C2×C16 | D21 | semidirect |
| 79. C3×C7 | C22⋊C16 | semidirect |
| 106. C7 | (C2×D3)⋊C16 | semidirect |
| 118. C3 | (C2×D7)⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D21 | 2 |
| C2×C3×C7×C16 | 2 |
| C2×C3⋊(C7⋊C16) | 2 |
| (C2×D7)⋊C16 | 3 |
| (C2×D3)⋊C16 | 7 |