Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
284 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 64 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. #10621434 | C2 | semidirect |
| 3. #10620938 | C2 | semidirect |
| 4. #10620884 | C2 | semidirect |
| 5. C3×#6411 | C2 | semidirect |
| 6. #10620514 | C2 | semidirect |
| 7. #10620497 | C2 | semidirect |
| 31. #6411 | D3 | semidirect |
| 173. C3×C7 | #456 | semidirect |
| 227. C7 | #4826 | semidirect |
| 242. C3 | #90018 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1010 | 2 |
| #10621434 | 2 |
| #10620938 | 2 |
| #10620884 | 2 |
| C3×#6411 | 2 |
| #10620514 | 2 |
| #10620497 | 2 |
| #90018 | 3 |
| #4826 | 7 |