Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 112 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. C22×C3⋊(C7⋊C8) | C2 | semidirect |
| 3. C3×#6489 | C2 | semidirect |
| 4. #10620507 | C2 | semidirect |
| 5. #10620501 | C2 | semidirect |
| 10. C7×#235 | C4 | semidirect |
| 20. #6489 | D3 | semidirect |
| 86. #235 | Dic7 | semidirect |
| 129. C3×C7 | #416 | semidirect |
| 171. C7 | #5002 | semidirect |
| 186. C3 | #90005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#235 | 2 |
| C22×C3⋊(C7⋊C8) | 2 |
| C3×#6489 | 2 |
| #10620507 | 2 |
| #10620501 | 2 |
| #90005 | 3 |
| #5002 | 7 |