Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
852 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 184 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×#4247 | C2 | semidirect |
| 3. C22×#4247 | C2 | semidirect |
| 4. C22×D21⋊C4 | C2 | semidirect |
| 5. C2×C7×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C2×C3×Dic7⋊C4 | C2 | semidirect |
| 7. C2×#66575 | C2 | semidirect |
| 8. #10620982 | C2 | direct (N × H) |
| 15. C2×D84 | C22 | semidirect |
| 21. C2×#4247 | C22 | semidirect |
| 22. C2×#4247 | C22 | semidirect |
| 24. C2×D21⋊C4 | C22 | semidirect |
| 25. C7×(C2×D3)⋊C4 | C22 | semidirect |
| 26. C3×Dic7⋊C4 | C22 | semidirect |
| 27. #66575 | C22 | semidirect |
| 34. C2×Dic7⋊C4 | D3 | semidirect |
| 43. C22×D21 | D4 | semidirect |
| 56. C2×C3×Dic7 | D4 | semidirect |
| 79. Dic7⋊C4 | C2×D3 | semidirect |
| 86. C2×(C2×D3)⋊C4 | D7 | semidirect |
| 99. C2×D21 | C2×D4 | semidirect |
| 106. C3×Dic7 | C2×D4 | semidirect |
| 129. C2×Dic7 | D12 | semidirect |
| 151. (C2×D3)⋊C4 | C2×D7 | semidirect |
| 152. C2×C3×C7 | #121 | semidirect |
| 186. Dic7 | C2×D12 | semidirect |
| 212. C3×C7 | C2×#121 | semidirect |
| 232. C2×C7 | #895 | semidirect |
| 283. C7 | C2×#895 | semidirect |
| 284. C2×C3 | #6447 | semidirect |
| 311. C3 | C2×#6447 | semidirect |
| 315. C2 | #10620982 | 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×#4247 | 2 |
| C22×D21⋊C4 | 2 |
| C2×C7×(C2×D3)⋊C4 | 2 |
| C2×C3×Dic7⋊C4 | 2 |
| C2×#66575 | 2 |
| #10620982 | 2 |
| C2×#6447 | 3 |
| C2×#895 | 7 |