Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
748 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 163 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×#11718854 | C2 | semidirect |
| 2. C22×D208 | C2 | semidirect |
| 3. #13125323 | C2 | semidirect |
| 4. #13123687 | C2 | semidirect |
| 5. #13116894 | C2 | semidirect |
| 6. #13116870 | C2 | semidirect |
| 7. #13116594 | C2 | semidirect |
| 8. #13116551 | C2 | semidirect |
| 9. C13×#2138 | C2 | semidirect |
| 19. #11718852 | C22 | semidirect |
| 20. C2×#88068 | C22 | semidirect |
| 22. #11718812 | C22 | semidirect |
| 23. C2×#88066 | C22 | semidirect |
| 29. #11718533 | C22 | semidirect |
| 31. C13×#358 | C22 | semidirect |
| 32. C13×#357 | C22 | semidirect |
| 33. #11718093 | C22 | semidirect |
| 34. #11718083 | C22 | semidirect |
| 59. C2×D104 | D4 | semidirect |
| 134. #2138 | D13 | semidirect |
| 190. #358 | C2×D13 | semidirect |
| 192. #357 | C2×D13 | semidirect |
| 306. C13 | #33585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718854 | 2 |
| C22×D208 | 2 |
| #13125323 | 2 |
| #13123687 | 2 |
| #13116894 | 2 |
| #13116870 | 2 |
| #13116594 | 2 |
| #13116551 | 2 |
| C13×#2138 | 2 |
| #33585 | 13 |