Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
252 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 158 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. C7×C4⋊(C3⋊C8) | C2 | semidirect |
| 15. #4924 | C7 | direct (N × H) |
| 34. C4⋊(C3⋊C8) | C2×C7 | semidirect |
| 40. C3×C4×C7 | M16 | semidirect |
| 70. C4×C7 | #208 | semidirect |
| 83. C3×C7 | #423 | semidirect |
| 99. C3×C4 | C7×M16 | semidirect |
| 111. C7 | #4924 | direct (N × H) |
| 119. C4 | C7×#208 | semidirect |
| 123. C3 | C7×#423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C42×C7 | 2 |
| C2×C7×#208 | 2 |
| C7×C4⋊(C3⋊C8) | 2 |
| C7×#423 | 3 |
| #4924 | 7 |