Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
244 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 74 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. #10620906 | C2 | semidirect |
| 4. C7×#810 | C2 | semidirect |
| 5. C3×#6382 | C2 | semidirect |
| 7. #10620486 | C2 | semidirect |
| 20. #66568 | C4 | semidirect |
| 27. #6382 | D3 | semidirect |
| 39. C7×Dic6 | C2×C4 | semidirect |
| 41. C3×C7⋊C8 | C2×C4 | semidirect |
| 60. #810 | D7 | semidirect |
| 70. Dic21 | SD16 | semidirect |
| 87. C7⋊C8 | C4×D3 | semidirect |
| 133. Dic6 | C4×D7 | semidirect |
| 136. C3×C7 | C4×SD16 | semidirect |
| 178. C7 | #4852 | semidirect |
| 194. C3 | #89560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621376 | 2 |
| #10620906 | 2 |
| C2×#66568 | 2 |
| C7×#810 | 2 |
| C3×#6382 | 2 |
| #10620503 | 2 |
| #10620486 | 2 |
| #89560 | 3 |
| #4852 | 7 |