Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
748 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 171 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×#11718808 | C2 | semidirect |
| 2. #13125317 | C2 | semidirect |
| 3. #13123688 | C2 | semidirect |
| 4. #13116889 | C2 | semidirect |
| 5. #13116869 | C2 | semidirect |
| 6. #13116594 | C2 | semidirect |
| 7. #13116552 | C2 | semidirect |
| 8. #13116544 | C2 | semidirect |
| 9. C22×C13×D16 | C2 | semidirect |
| 20. #11718816 | C22 | semidirect |
| 23. #11718812 | C22 | semidirect |
| 24. D8×Dic13 | C22 | semidirect |
| 25. C2×#88067 | C22 | semidirect |
| 27. C2×#88066 | C22 | semidirect |
| 31. #11718154 | C22 | semidirect |
| 32. #11718101 | C22 | semidirect |
| 33. #11718095 | C22 | semidirect |
| 34. #11718093 | C22 | semidirect |
| 43. C2×C13×D8 | D4 | semidirect |
| 127. C22×D16 | D13 | semidirect |
| 226. C2×D8 | C22⋊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×#11718808 | 2 |
| #13125317 | 2 |
| #13123688 | 2 |
| #13116889 | 2 |
| #13116869 | 2 |
| #13116594 | 2 |
| #13116552 | 2 |
| #13116544 | 2 |
| C22×C13×D16 | 2 |
| #33585 | 13 |