Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 78 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. C3×#6456 | C2 | semidirect |
| 2. #10620980 | C2 | semidirect |
| 4. #10620648 | C2 | semidirect |
| 5. C7×#807 | C2 | semidirect |
| 6. #10620499 | C2 | semidirect |
| 7. C3⋊C8×Dic7 | C2 | semidirect |
| 20. #66561 | C4 | semidirect |
| 23. #6456 | D3 | semidirect |
| 34. D84 | C2×C4 | semidirect |
| 39. C3×D28 | C2×C4 | semidirect |
| 43. C7×C3⋊C8 | C2×C4 | semidirect |
| 61. #807 | D7 | semidirect |
| 74. C3×Dic7 | D8 | semidirect |
| 87. D28 | C4×D3 | semidirect |
| 128. Dic7 | #213 | semidirect |
| 143. C3⋊C8 | C4×D7 | semidirect |
| 144. C3×C7 | C4×D8 | semidirect |
| 190. C7 | C4×#213 | semidirect |
| 209. C3 | #89644 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6456 | 2 |
| #10620980 | 2 |
| C2×#66561 | 2 |
| #10620648 | 2 |
| C7×#807 | 2 |
| #10620499 | 2 |
| C3⋊C8×Dic7 | 2 |
| #89644 | 3 |
| C4×#213 | 7 |