Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
380 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 96 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. #10620900 | C2 | semidirect |
| 3. C2×#66558 | C2 | semidirect |
| 4. #10620671 | C2 | semidirect |
| 5. C3×#6406 | C2 | semidirect |
| 6. #10620502 | C2 | semidirect |
| 7. #10620501 | C2 | semidirect |
| 13. D3×C7×D4 | C4 | semidirect |
| 16. C4⋊Dic21 | C22 | semidirect |
| 17. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 18. C3×C4⋊Dic7 | C22 | semidirect |
| 19. C2×C3×C7⋊C8 | C22 | semidirect |
| 29. #6406 | D3 | semidirect |
| 59. C4⋊Dic7 | C2×D3 | semidirect |
| 63. C2×C7⋊C8 | C2×D3 | semidirect |
| 111. D3×D4 | Dic7 | semidirect |
| 169. C3×C7 | #418 | semidirect |
| 225. C7 | #4770 | semidirect |
| 248. C3 | #89987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C7×D4 | 2 |
| #10620900 | 2 |
| C2×#66558 | 2 |
| #10620671 | 2 |
| C3×#6406 | 2 |
| #10620502 | 2 |
| #10620501 | 2 |
| #89987 | 3 |
| #4770 | 7 |