Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
252 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 4. C7×Dic3⋊C8 | C2 | semidirect |
| 19. #5118 | C7 | direct (N × H) |
| 42. Dic3⋊C8 | C2×C7 | semidirect |
| 50. C7×Dic3 | M16 | semidirect |
| 96. C3×C7 | #423 | semidirect |
| 116. Dic3 | C7×M16 | semidirect |
| 127. C7 | #5118 | direct (N × H) |
| 139. 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×C7×M16 | 2 |
| C2×C4×C7×Dic3 | 2 |
| C2×C7×#208 | 2 |
| C7×Dic3⋊C8 | 2 |
| C7×#423 | 3 |
| #5118 | 7 |