Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
112 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 47 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. C3×C7×M32 | C2 | semidirect |
| 3. C2×C3⋊(C7⋊C16) | C2 | semidirect |
| 13. C7×M32 | D3 | semidirect |
| 32. C3×M32 | D7 | semidirect |
| 59. M32 | D21 | semidirect |
| 74. C3×C7 | #350 | semidirect |
| 98. C7 | #4515 | semidirect |
| 107. C3 | #89310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621384 | 2 |
| C3×C7×M32 | 2 |
| C2×C3⋊(C7⋊C16) | 2 |
| #89310 | 3 |
| #4515 | 7 |