Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
284 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 144 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. #10620487 | C2 | semidirect |
| 5. C3⋊C8×Dic7 | C2 | semidirect |
| 9. #66627 | C4 | semidirect |
| 11. C7×#208 | C4 | semidirect |
| 30. C3⋊(C7⋊C8) | C2×C4 | semidirect |
| 31. C7×C3⋊C8 | C2×C4 | semidirect |
| 53. C3×Dic7 | M16 | semidirect |
| 71. #208 | Dic7 | direct (N × H) |
| 89. Dic7 | #208 | direct (N × H) |
| 99. C3⋊C8 | C2×Dic7 | semidirect |
| 100. C3×C7 | C4×M16 | semidirect |
| 131. C7 | C4×#208 | semidirect |
| 143. C3 | M16×Dic7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66627 | 2 |
| C2×C7×#208 | 2 |
| C2×C3×C4×Dic7 | 2 |
| #10620487 | 2 |
| C3⋊C8×Dic7 | 2 |
| M16×Dic7 | 3 |
| C4×#208 | 7 |