Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
516 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 3. C2×Dic3×Dic7 | C2 | semidirect |
| 4. C7×C3⋊#95 | C2 | semidirect |
| 5. C3×C7⋊#95 | C2 | semidirect |
| 11. C2×C4×D21 | C4 | semidirect |
| 14. #66575 | C4 | semidirect |
| 20. C7⋊#95 | D3 | semidirect |
| 35. C2×C7×Dic3 | C2×C4 | semidirect |
| 38. C2×C3×Dic7 | C2×C4 | semidirect |
| 52. C3⋊#95 | D7 | semidirect |
| 62. C2×D21 | C42 | semidirect |
| 64. Dic21 | C22⋊C4 | semidirect |
| 83. C2×Dic7 | C4×D3 | semidirect |
| 134. C2×Dic3 | C4×D7 | semidirect |
| 136. C3×C7 | C4×C22⋊C4 | semidirect |
| 183. C7 | #4666 | semidirect |
| 204. C3 | #89438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D21 | 2 |
| C2×#66575 | 2 |
| C2×Dic3×Dic7 | 2 |
| C7×C3⋊#95 | 2 |
| C3×C7⋊#95 | 2 |
| #89438 | 3 |
| #4666 | 7 |