Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
852 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 192 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×C7×D12 | C2 | semidirect |
| 2. C22×#4247 | C2 | semidirect |
| 3. C22×#4247 | C2 | semidirect |
| 4. C22×D3×Dic7 | C2 | semidirect |
| 5. C2×#66631 | C2 | semidirect |
| 6. C2×C3×Dic7⋊C4 | C2 | semidirect |
| 7. C2×(C2×D3)⋊Dic7 | C2 | semidirect |
| 8. #10620978 | C2 | direct (N × H) |
| 16. C2×C7×D12 | C22 | semidirect |
| 21. C2×#4247 | C22 | semidirect |
| 22. C2×#4247 | C22 | semidirect |
| 24. C2×D3×Dic7 | C22 | semidirect |
| 25. #66631 | C22 | semidirect |
| 26. C3×Dic7⋊C4 | C22 | semidirect |
| 27. (C2×D3)⋊Dic7 | C22 | semidirect |
| 35. C2×Dic7⋊C4 | D3 | semidirect |
| 47. C22×D3×C7 | D4 | semidirect |
| 56. C2×C3×Dic7 | D4 | semidirect |
| 79. Dic7⋊C4 | C2×D3 | semidirect |
| 82. C22×D12 | D7 | semidirect |
| 103. C2×D3×C7 | C2×D4 | semidirect |
| 107. C3×Dic7 | C2×D4 | semidirect |
| 131. C2×Dic7 | D12 | semidirect |
| 146. C2×D12 | C2×D7 | semidirect |
| 152. C2×C3×C7 | #121 | semidirect |
| 186. Dic7 | C2×D12 | semidirect |
| 197. C22×D3 | C22⋊D7 | semidirect |
| 212. C3×C7 | C2×#121 | semidirect |
| 233. C2×C7 | #895 | semidirect |
| 253. C2×D3 | C2×C22⋊D7 | semidirect |
| 283. C7 | C2×#895 | semidirect |
| 284. C2×C3 | #6502 | semidirect |
| 311. C3 | C2×#6502 | semidirect |
| 315. C2 | #10620978 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D12 | 2 |
| C22×#4247 | 2 |
| C22×D3×Dic7 | 2 |
| C2×#66631 | 2 |
| C2×C3×Dic7⋊C4 | 2 |
| C2×(C2×D3)⋊Dic7 | 2 |
| #10620978 | 2 |
| C2×#6502 | 3 |
| C2×#895 | 7 |