Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
516 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 2. C2×C3×C42×C7 | C2 | semidirect |
| 3. C2×#66631 | C2 | semidirect |
| 4. C2×C4⋊Dic21 | C2 | semidirect |
| 12. C2×D84 | C4 | semidirect |
| 17. C2×C42×C7 | D3 | semidirect |
| 32. C2×C3×C4×C7 | D4 | semidirect |
| 47. C2×C3×C42 | D7 | semidirect |
| 61. C3×C4×C7 | C22⋊C4 | semidirect |
| 74. C2×C4×C7 | D12 | semidirect |
| 98. C2×C42 | D21 | semidirect |
| 110. C4×C7 | (C2×D3)⋊C4 | semidirect |
| 122. C2×C3×C4 | D28 | semidirect |
| 127. C3×C7 | #390 | semidirect |
| 155. C3×C4 | (C2×D7)⋊C4 | semidirect |
| 170. C2×C4 | D84 | semidirect |
| 172. C7 | #4939 | semidirect |
| 191. C4 | #66631 | semidirect |
| 192. C3 | #89711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D84 | 2 |
| C2×C3×C42×C7 | 2 |
| C2×#66631 | 2 |
| C2×C4⋊Dic21 | 2 |
| #89711 | 3 |
| #4939 | 7 |