Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
852 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 211 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. C22×D84 | C2 | semidirect |
| 2. C22×D84 | C2 | semidirect |
| 3. C22×C4×D21 | C2 | semidirect |
| 4. C2×C3×C7×C4⋊C4 | C2 | semidirect |
| 5. C2×#66631 | C2 | semidirect |
| 6. #10621378 | C2 | direct (N × H) |
| 15. C2×D84 | C22 | semidirect |
| 16. C2×D84 | C22 | semidirect |
| 18. C2×C4×D21 | C22 | semidirect |
| 19. C3×C7×C4⋊C4 | C22 | semidirect |
| 20. #66631 | C22 | semidirect |
| 24. C2×C7×C4⋊C4 | D3 | semidirect |
| 34. C22×D21 | D4 | semidirect |
| 38. C2×C3×C4×C7 | D4 | semidirect |
| 57. C7×C4⋊C4 | C2×D3 | semidirect |
| 62. C2×C3×C4⋊C4 | D7 | semidirect |
| 76. C2×D21 | C2×D4 | semidirect |
| 78. C3×C4×C7 | C2×D4 | semidirect |
| 91. C2×C4×C7 | D12 | semidirect |
| 110. C3×C4⋊C4 | C2×D7 | semidirect |
| 112. C2×C3×C7 | #121 | semidirect |
| 122. C2×C4⋊C4 | D21 | semidirect |
| 137. C4×C7 | C2×D12 | semidirect |
| 149. C2×C3×C4 | D28 | semidirect |
| 157. C3×C7 | C2×#121 | semidirect |
| 169. C4⋊C4 | C2×D21 | semidirect |
| 171. C2×C7 | #895 | semidirect |
| 190. C3×C4 | C2×D28 | semidirect |
| 207. C2×C4 | D84 | semidirect |
| 210. C7 | C2×#895 | semidirect |
| 211. C2×C3 | #6458 | semidirect |
| 231. C4 | C2×D84 | semidirect |
| 232. C3 | C2×#6458 | semidirect |
| 235. C2 | #10621378 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D84 | 2 |
| C22×C4×D21 | 2 |
| C2×C3×C7×C4⋊C4 | 2 |
| C2×#66631 | 2 |
| #10621378 | 2 |
| C2×#6458 | 3 |
| C2×#895 | 7 |