Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
2118 conjugacy classes of subgroups; only the 587 normal subgroups are shown.
This group has 2118 conjugacy classes of subgroups — too many to draw. Only its 587 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. C22×#88166 | C2 | semidirect |
| 2. C2×#11718573 | C2 | direct (N × H) |
| 3. C22×Dic104 | C2 | semidirect |
| 4. C22×#88067 | C2 | semidirect |
| 5. C22×C16×D13 | C2 | semidirect |
| 6. C22×C13×D16 | C2 | semidirect |
| 11. C2×#88166 | C22 | semidirect |
| 14. C2×C13×D16 | C22 | semidirect |
| 16. C2×#88067 | C22 | semidirect |
| 18. #11718573 | C22 | direct (N × H) |
| 19. C2×Dic104 | C22 | semidirect |
| 20. C2×C16×D13 | C22 | semidirect |
| 34. #88166 | C23 | semidirect |
| 39. C13×D16 | C23 | semidirect |
| 41. #88067 | C23 | semidirect |
| 43. Dic104 | C23 | semidirect |
| 44. C16×D13 | C23 | semidirect |
| 77. C22×D16 | D13 | semidirect |
| 109. C2×D16 | C2×D13 | semidirect |
| 115. C22×C13 | #508 | semidirect |
| 143. D16 | C22×D13 | semidirect |
| 148. C2×C13 | C2×#508 | semidirect |
| 178. C13 | C22×#508 | semidirect |
| 203. C22 | #11718573 | direct (N × H) |
| 211. C2 | C2×#11718573 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88166 | 2 |
| C2×#11718573 | 2 |
| C22×Dic104 | 2 |
| C22×#88067 | 2 |
| C22×C16×D13 | 2 |
| C22×C13×D16 | 2 |
| C22×#508 | 13 |