Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 78 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. #10621375 | C2 | semidirect |
| 3. C2×D21⋊C8 | C2 | semidirect |
| 4. C7×#809 | C2 | semidirect |
| 5. C3×#6384 | C2 | semidirect |
| 6. #10620506 | C2 | semidirect |
| 7. #10620502 | C2 | semidirect |
| 15. #66672 | C4 | semidirect |
| 29. #6384 | D3 | semidirect |
| 68. #809 | D7 | semidirect |
| 156. C3×C7 | #416 | semidirect |
| 206. C7 | #4804 | semidirect |
| 225. C3 | #89544 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66672 | 2 |
| #10621375 | 2 |
| C2×D21⋊C8 | 2 |
| C7×#809 | 2 |
| C3×#6384 | 2 |
| #10620506 | 2 |
| #10620502 | 2 |
| #89544 | 3 |
| #4804 | 7 |