Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
168 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 1. C7×#904 | C2 | semidirect |
| 2. C3×#6467 | C2 | semidirect |
| 3. C2×C3⋊(C7⋊C16) | C2 | semidirect |
| 4. #10620481 | C2 | semidirect |
| 5. #10620476 | C2 | semidirect |
| 6. #10620475 | C2 | semidirect |
| 7. #10620472 | C2 | semidirect |
| 21. #6467 | D3 | semidirect |
| 51. #904 | D7 | semidirect |
| 116. C3×C7 | #508 | semidirect |
| 150. C7 | #5194 | semidirect |
| 162. C3 | #89966 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#904 | 2 |
| C3×#6467 | 2 |
| C2×C3⋊(C7⋊C16) | 2 |
| #10620481 | 2 |
| #10620476 | 2 |
| #10620475 | 2 |
| #10620472 | 2 |
| #89966 | 3 |
| #5194 | 7 |