Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
852 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 187 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×#4268 | C2 | semidirect |
| 2. C22×#4268 | C2 | semidirect |
| 3. C22×D84 | C2 | semidirect |
| 4. C22×C4×D21 | C2 | semidirect |
| 5. C2×C3×C7×C22⋊C4 | C2 | semidirect |
| 6. C2×#66631 | C2 | semidirect |
| 7. C2×#66629 | C2 | semidirect |
| 8. #10621367 | C2 | direct (N × H) |
| 17. C2×#4268 | C22 | semidirect |
| 18. C2×#4268 | C22 | semidirect |
| 22. C2×D84 | C22 | semidirect |
| 24. C2×C4×D21 | C22 | semidirect |
| 25. C3×C7×C22⋊C4 | C22 | semidirect |
| 26. #66631 | C22 | semidirect |
| 27. #66629 | C22 | semidirect |
| 32. C2×C7×C22⋊C4 | D3 | semidirect |
| 47. C22×D21 | D4 | semidirect |
| 57. C2×Dic21 | D4 | semidirect |
| 77. C7×C22⋊C4 | C2×D3 | semidirect |
| 84. C2×C3×C22⋊C4 | D7 | semidirect |
| 103. C2×D21 | C2×D4 | semidirect |
| 107. Dic21 | C2×D4 | semidirect |
| 149. C3×C22⋊C4 | C2×D7 | semidirect |
| 153. C2×C3×C7 | #121 | semidirect |
| 166. C2×C22⋊C4 | D21 | semidirect |
| 212. C3×C7 | C2×#121 | semidirect |
| 230. C22⋊C4 | C2×D21 | semidirect |
| 232. C2×C7 | #884 | semidirect |
| 283. C7 | C2×#884 | semidirect |
| 285. C2×C3 | #6447 | semidirect |
| 311. C3 | C2×#6447 | semidirect |
| 315. C2 | #10621367 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4268 | 2 |
| C22×D84 | 2 |
| C22×C4×D21 | 2 |
| C2×C3×C7×C22⋊C4 | 2 |
| C2×#66631 | 2 |
| C2×#66629 | 2 |
| #10621367 | 2 |
| C2×#6447 | 3 |
| C2×#884 | 7 |