Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×#66673 | C2 | semidirect |
| 2. C7×#895 | C2 | semidirect |
| 3. C2×#66564 | C2 | semidirect |
| 4. C2×#66562 | C2 | semidirect |
| 5. #10620648 | C2 | semidirect |
| 6. C3×#6384 | C2 | semidirect |
| 7. (C2×D3)⋊(C7⋊C8) | C2 | semidirect |
| 29. #6384 | D3 | semidirect |
| 38. D84 | D4 | semidirect |
| 47. C3×Dic14 | D4 | semidirect |
| 70. #895 | D7 | semidirect |
| 107. Dic14 | D12 | semidirect |
| 173. C3×C7 | #449 | semidirect |
| 230. C7 | #4810 | semidirect |
| 252. C3 | #89809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66673 | 2 |
| C7×#895 | 2 |
| C2×#66564 | 2 |
| C2×#66562 | 2 |
| #10620648 | 2 |
| C3×#6384 | 2 |
| (C2×D3)⋊(C7⋊C8) | 2 |
| #89809 | 3 |
| #4810 | 7 |