Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
542 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 139 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×D13×D16 | C2 | semidirect |
| 2. C2×D416 | C2 | semidirect |
| 3. C2×#11718111 | C2 | semidirect |
| 4. D13×D32 | C2 | direct (N × H) |
| 5. C2×D13×C32 | C2 | semidirect |
| 6. C2×C13×D32 | C2 | semidirect |
| 8. C2×C13×D16 | C22 | semidirect |
| 11. D13×D16 | C22 | semidirect |
| 12. C2×D208 | C22 | semidirect |
| 14. C13×D32 | C22 | semidirect |
| 15. C2×C13×C32 | C22 | semidirect |
| 16. #11718111 | C22 | semidirect |
| 17. C2×#88034 | C22 | semidirect |
| 18. D416 | C22 | semidirect |
| 19. D13×C32 | C22 | semidirect |
| 28. C13×D16 | C23 | semidirect |
| 33. D208 | C23 | semidirect |
| 36. C13×C32 | C23 | semidirect |
| 37. #88034 | C23 | semidirect |
| 62. C2×D32 | D13 | direct (N × H) |
| 86. C2×D16 | C2×D13 | semidirect |
| 90. D32 | C2×D13 | direct (N × H) |
| 93. C2×C32 | C2×D13 | semidirect |
| 100. C2×D13 | D32 | direct (N × H) |
| 116. D16 | C22×D13 | semidirect |
| 122. C32 | C22×D13 | semidirect |
| 124. C2×C13 | C2×D32 | semidirect |
| 127. D13 | C2×D32 | direct (N × H) |
| 147. C13 | C22×D32 | semidirect |
| 179. C2 | D13×D32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D13×D16 | 2 |
| C2×D416 | 2 |
| C2×#11718111 | 2 |
| D13×D32 | 2 |
| C2×D13×C32 | 2 |
| C2×C13×D32 | 2 |
| C22×D32 | 13 |