Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
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×#10596962 | C2 | semidirect |
| 2. C22×D148 | C2 | semidirect |
| 3. #11924564 | C2 | direct (N × H) |
| 4. C2×#10596930 | C2 | semidirect |
| 5. C2×D296 | C2 | semidirect |
| 6. C2×M16×C37 | C2 | semidirect |
| 11. #10596962 | C22 | semidirect |
| 15. C2×D148 | C22 | semidirect |
| 16. C2×D148 | C22 | semidirect |
| 18. C2×Dic74 | C22 | semidirect |
| 19. M16×C37 | C22 | semidirect |
| 20. C2×C8×C37 | C22 | semidirect |
| 21. D296 | C22 | semidirect |
| 22. #10596930 | C22 | semidirect |
| 38. D148 | C23 | semidirect |
| 41. Dic74 | C23 | semidirect |
| 42. C8×C37 | C23 | semidirect |
| 56. C2×C37 | AGL(1,ℤ/8) | semidirect |
| 61. C37 | C2×AGL(1,ℤ/8) | semidirect |
| 67. C2×M16 | D37 | semidirect |
| 82. M16 | C2×D37 | semidirect |
| 83. C2×C8 | C2×D37 | semidirect |
| 103. C8 | C22×D37 | semidirect |
| 119. C2 | #11924564 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10596962 | 2 |
| C22×D148 | 2 |
| #11924564 | 2 |
| C2×#10596930 | 2 |
| C2×D296 | 2 |
| C2×M16×C37 | 2 |
| C2×AGL(1,ℤ/8) | 37 |