Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
220 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 61 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. #10621373 | C2 | semidirect |
| 3. C3×C7×#102 | C2 | semidirect |
| 4. #10620671 | C2 | semidirect |
| 5. #10620660 | C2 | semidirect |
| 6. #10620654 | C2 | semidirect |
| 7. #10620648 | C2 | semidirect |
| 22. C7×#102 | D3 | semidirect |
| 56. C3×#102 | D7 | semidirect |
| 111. #102 | D21 | semidirect |
| 141. C3×C7 | #490 | semidirect |
| 186. C7 | #4764 | semidirect |
| 205. C3 | #89536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621423 | 2 |
| #10621373 | 2 |
| C3×C7×#102 | 2 |
| #10620671 | 2 |
| #10620660 | 2 |
| #10620654 | 2 |
| #10620648 | 2 |
| #89536 | 3 |
| #4764 | 7 |