Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
516 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 168 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×C4×C7×Dic3 | C2 | semidirect |
| 3. C2×C3×C4×Dic7 | C2 | semidirect |
| 5. #10620529 | C2 | semidirect |
| 12. C2×C4×D21 | C4 | semidirect |
| 17. #66575 | C4 | direct (N × H) |
| 21. C2×C4×Dic7 | D3 | semidirect |
| 39. C2×C7×Dic3 | C2×C4 | semidirect |
| 42. C2×C3×Dic7 | C2×C4 | semidirect |
| 57. C2×C4×Dic3 | D7 | semidirect |
| 68. C2×D21 | C42 | semidirect |
| 69. C3×C4×C7 | C22⋊C4 | semidirect |
| 91. C2×Dic7 | C4×D3 | semidirect |
| 126. C4×C7 | (C2×D3)⋊C4 | semidirect |
| 146. C2×Dic3 | C4×D7 | semidirect |
| 148. C3×C7 | C4×C22⋊C4 | semidirect |
| 177. C3×C4 | (C2×D7)⋊C4 | semidirect |
| 199. C7 | C4×(C2×D3)⋊C4 | semidirect |
| 219. C4 | #66575 | direct (N × H) |
| 220. C3 | C4×(C2×D7)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D21 | 2 |
| C2×C4×C7×Dic3 | 2 |
| C2×C3×C4×Dic7 | 2 |
| C2×#66575 | 2 |
| #10620529 | 2 |
| C4×(C2×D7)⋊C4 | 3 |
| C4×(C2×D3)⋊C4 | 7 |