Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
236 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 122 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. C3×Dic7⋊C8 | C2 | semidirect |
| 5. C3×C8×Dic7 | C2 | semidirect |
| 6. #89490 | C3 | direct (N × H) |
| 19. Dic7⋊C8 | C2×C3 | semidirect |
| 20. C8×Dic7 | C2×C3 | semidirect |
| 27. C2×C3×Dic7 | C8 | semidirect |
| 64. C2×Dic7 | C3×C8 | semidirect |
| 111. C3×C7 | #431 | semidirect |
| 147. C7 | C3×#431 | semidirect |
| 162. C3 | #89490 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×Dic7 | 2 |
| C3×C7×C22⋊C8 | 2 |
| C3×C22⋊(C7⋊C8) | 2 |
| C3×Dic7⋊C8 | 2 |
| C3×C8×Dic7 | 2 |
| #89490 | 3 |
| C3×#431 | 7 |