Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 54 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×#6471 | C2 | semidirect |
| 2. #10620861 | C2 | semidirect |
| 3. C2×#66560 | C2 | semidirect |
| 4. #10620846 | C2 | semidirect |
| 5. #10620661 | C2 | semidirect |
| 6. C7×#823 | C2 | semidirect |
| 7. #10620493 | C2 | semidirect |
| 26. #6471 | D3 | semidirect |
| 68. #823 | D7 | semidirect |
| 148. C3×C7 | #472 | semidirect |
| 194. C7 | #5199 | semidirect |
| 209. C3 | #89521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6471 | 2 |
| #10620861 | 2 |
| C2×#66560 | 2 |
| #10620846 | 2 |
| #10620661 | 2 |
| C7×#823 | 2 |
| #10620493 | 2 |
| #89521 | 3 |
| #5199 | 7 |