Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 248 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 |
|---|---|---|
| 1. C3×#6456 | C2 | semidirect |
| 2. #10620935 | C2 | semidirect |
| 3. C2×#66565 | C2 | semidirect |
| 5. #10620649 | C2 | semidirect |
| 6. C7×#809 | C2 | semidirect |
| 7. Dic7⋊(C3⋊C8) | C2 | semidirect |
| 25. #6456 | D3 | semidirect |
| 64. #809 | D7 | semidirect |
| 150. C3×C7 | #463 | semidirect |
| 198. C7 | #5016 | semidirect |
| 217. C3 | #89559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6456 | 2 |
| #10620935 | 2 |
| C2×#66565 | 2 |
| C2×#66560 | 2 |
| #10620649 | 2 |
| C7×#809 | 2 |
| Dic7⋊(C3⋊C8) | 2 |
| #89559 | 3 |
| #5016 | 7 |