Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
836 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 272 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 |
|---|---|---|
| 3. C2×C7×C4⋊Dic3 | C2 | semidirect |
| 4. C2×C3×C4⋊Dic7 | C2 | semidirect |
| 5. C2×#66577 | C2 | semidirect |
| 6. #10620999 | C2 | direct (N × H) |
| 11. C2×C4×D21 | C4 | semidirect |
| 17. C7×C4⋊Dic3 | C22 | semidirect |
| 18. C3×C4⋊Dic7 | C22 | semidirect |
| 19. #66577 | C22 | semidirect |
| 23. C2×C4⋊Dic7 | D3 | semidirect |
| 32. C2×C3×C4×C7 | C2×C4 | semidirect |
| 34. C2×Dic21 | C2×C4 | semidirect |
| 36. C4×D21 | C2×C4 | semidirect |
| 52. C4⋊Dic7 | C2×D3 | semidirect |
| 57. C2×C4⋊Dic3 | D7 | semidirect |
| 64. C2×D21 | C4⋊C4 | semidirect |
| 68. C3×C4×C7 | C22×C4 | semidirect |
| 69. Dic21 | C22×C4 | semidirect |
| 80. C2×C4×C7 | C4×D3 | semidirect |
| 98. C4⋊Dic3 | C2×D7 | semidirect |
| 100. C2×C3×C7 | C2×C4⋊C4 | semidirect |
| 104. D21 | C2×C4⋊C4 | semidirect |
| 120. C4×C7 | C2×C4×D3 | semidirect |
| 130. C2×C3×C4 | C4×D7 | semidirect |
| 138. C3×C7 | C22×C4⋊C4 | semidirect |
| 151. C2×C7 | D3×C4⋊C4 | semidirect |
| 165. C3×C4 | C2×C4×D7 | semidirect |
| 181. C2×C4 | D21⋊C4 | semidirect |
| 183. C7 | C2×D3×C4⋊C4 | semidirect |
| 184. C2×C3 | D7×C4⋊C4 | semidirect |
| 200. C4 | C2×D21⋊C4 | semidirect |
| 201. C3 | C2×D7×C4⋊C4 | semidirect |
| 203. C2 | #10620999 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D21 | 2 |
| C22×D21⋊C4 | 2 |
| C2×C7×C4⋊Dic3 | 2 |
| C2×C3×C4⋊Dic7 | 2 |
| C2×#66577 | 2 |
| #10620999 | 2 |
| C2×D7×C4⋊C4 | 3 |
| C2×D3×C4⋊C4 | 7 |