Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
2590 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2590 conjugacy classes of subgroups — too many to draw. Only its 747 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. C23×D104 | C2 | semidirect |
| 2. C22×D208 | C2 | direct (N × H) |
| 3. C23×C13×C16 | C2 | semidirect |
| 7. C22×D104 | C22 | semidirect |
| 8. C22×C13×C16 | C22 | semidirect |
| 9. C2×D208 | C22 | direct (N × H) |
| 17. C2×D104 | C23 | semidirect |
| 18. C2×C13×C16 | C23 | semidirect |
| 19. D208 | C23 | direct (N × H) |
| 31. D104 | C24 | semidirect |
| 32. C13×C16 | C24 | semidirect |
| 35. C23×C16 | D13 | semidirect |
| 36. C23×C13 | D16 | semidirect |
| 51. C22×C16 | C2×D13 | semidirect |
| 52. C22×C13 | C2×D16 | semidirect |
| 67. C2×C16 | C22×D13 | semidirect |
| 68. C2×C13 | C22×D16 | semidirect |
| 82. C16 | C23×D13 | semidirect |
| 83. C13 | C23×D16 | semidirect |
| 86. C23 | D208 | direct (N × H) |
| 96. C22 | C2×D208 | direct (N × H) |
| 101. C2 | C22×D208 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D104 | 2 |
| C22×D208 | 2 |
| C23×C13×C16 | 2 |
| C23×D16 | 13 |