Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
532 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 160 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. C2×#66728 | C2 | semidirect |
| 2. C2×C3×#1157 | C2 | semidirect |
| 3. C22×C7×C3⋊C8 | C2 | semidirect |
| 4. C2×#66570 | C2 | semidirect |
| 5. C2×#66566 | C2 | semidirect |
| 6. #10620873 | C2 | direct (N × H) |
| 7. C2×#66565 | C2 | semidirect |
| 8. C2×#66561 | C2 | semidirect |
| 13. #66728 | C22 | semidirect |
| 19. C3×#1157 | C22 | semidirect |
| 25. C2×C7×C3⋊C8 | C22 | semidirect |
| 26. #66570 | C22 | semidirect |
| 27. #66566 | C22 | semidirect |
| 28. #66565 | C22 | semidirect |
| 29. #66561 | C22 | semidirect |
| 31. C2×#1157 | D3 | semidirect |
| 68. #1157 | C2×D3 | semidirect |
| 89. C22×C3⋊C8 | D7 | semidirect |
| 145. C2×C3⋊C8 | C2×D7 | semidirect |
| 147. C2×C3×C7 | #135 | semidirect |
| 194. C3×C7 | C2×#135 | semidirect |
| 216. C2×C7 | #950 | semidirect |
| 255. C7 | C2×#950 | semidirect |
| 258. C2×C3 | #6467 | semidirect |
| 273. C3 | C2×#6467 | semidirect |
| 277. C2 | #10620873 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66728 | 2 |
| C2×C3×#1157 | 2 |
| C22×C7×C3⋊C8 | 2 |
| C2×#66570 | 2 |
| C2×#66566 | 2 |
| #10620873 | 2 |
| C2×#66565 | 2 |
| C2×#66561 | 2 |
| C2×#6467 | 3 |
| C2×#950 | 7 |