Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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×#10625350 | C2 | semidirect |
| 2. C22×D188 | C2 | semidirect |
| 3. #13094052 | C2 | direct (N × H) |
| 4. C2×#10625325 | C2 | semidirect |
| 5. C2×D376 | C2 | semidirect |
| 6. C2×M16×C47 | C2 | semidirect |
| 11. #10625350 | C22 | semidirect |
| 15. C2×D188 | C22 | semidirect |
| 16. C2×D188 | C22 | semidirect |
| 18. C2×Dic94 | C22 | semidirect |
| 19. M16×C47 | C22 | semidirect |
| 20. C2×C8×C47 | C22 | semidirect |
| 21. D376 | C22 | semidirect |
| 22. #10625325 | C22 | semidirect |
| 38. D188 | C23 | semidirect |
| 41. Dic94 | C23 | semidirect |
| 42. C8×C47 | C23 | semidirect |
| 56. C2×C47 | AGL(1,ℤ/8) | semidirect |
| 61. C47 | C2×AGL(1,ℤ/8) | semidirect |
| 67. C2×M16 | D47 | semidirect |
| 82. M16 | C2×D47 | semidirect |
| 83. C2×C8 | C2×D47 | semidirect |
| 103. C8 | C22×D47 | semidirect |
| 119. C2 | #13094052 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625350 | 2 |
| C22×D188 | 2 |
| #13094052 | 2 |
| C2×#10625325 | 2 |
| C2×D376 | 2 |
| C2×M16×C47 | 2 |
| C2×AGL(1,ℤ/8) | 47 |