Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
204 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 4. C7×#822 | C2 | semidirect |
| 5. C3×#6396 | C2 | semidirect |
| 6. #10620528 | C2 | semidirect |
| 7. #10620526 | C2 | semidirect |
| 27. #6396 | D3 | semidirect |
| 61. #822 | D7 | semidirect |
| 130. C3×C7 | #430 | semidirect |
| 169. C7 | #4893 | semidirect |
| 182. C3 | #89665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M16×D21 | 2 |
| C2×#66559 | 2 |
| #10620854 | 2 |
| C7×#822 | 2 |
| C3×#6396 | 2 |
| #10620528 | 2 |
| #10620526 | 2 |
| #89665 | 3 |
| #4893 | 7 |