Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #10621376 | C2 | semidirect |
| 3. C3×C7×#107 | C2 | semidirect |
| 4. C8×Dic21 | C2 | semidirect |
| 5. #10620648 | C2 | semidirect |
| 14. D168 | C4 | semidirect |
| 17. C7×#107 | D3 | semidirect |
| 27. D84 | C2×C4 | semidirect |
| 29. C3×C7×C8 | C2×C4 | semidirect |
| 41. C3×#107 | D7 | semidirect |
| 52. Dic21 | D8 | semidirect |
| 62. C7×C8 | C4×D3 | semidirect |
| 78. #107 | D21 | semidirect |
| 98. C3×C8 | C4×D7 | semidirect |
| 100. C3×C7 | C4×D8 | semidirect |
| 131. C8 | C4×D21 | semidirect |
| 132. C7 | #4872 | semidirect |
| 146. C3 | #89644 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D168 | 2 |
| #10621376 | 2 |
| C3×C7×#107 | 2 |
| C8×Dic21 | 2 |
| #10620648 | 2 |
| #89644 | 3 |
| #4872 | 7 |