Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. C2×Dic84 | C2 | semidirect |
| 3. C2×C3×C7×C16 | C2 | semidirect |
| 4. #10620639 | C2 | direct (N × H) |
| 10. Dic84 | C22 | semidirect |
| 13. C3×C7×C16 | C22 | semidirect |
| 16. C2×C7×C16 | D3 | semidirect |
| 35. C7×C16 | C2×D3 | semidirect |
| 38. C2×C3×C16 | D7 | semidirect |
| 63. C3×C16 | C2×D7 | semidirect |
| 64. C2×C3×C7 | SD32 | semidirect |
| 70. C2×C16 | D21 | semidirect |
| 86. C3×C7 | C2×SD32 | semidirect |
| 94. C16 | C2×D21 | semidirect |
| 95. C2×C7 | #800 | semidirect |
| 113. C7 | C2×#800 | semidirect |
| 114. C2×C3 | #6374 | semidirect |
| 123. C3 | C2×#6374 | semidirect |
| 125. C2 | #10620639 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic84 | 2 |
| C2×D168 | 2 |
| C2×C3×C7×C16 | 2 |
| #10620639 | 2 |
| C2×#6374 | 3 |
| C2×#800 | 7 |