Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
668 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 135 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. #13127973 | C2 | semidirect |
| 2. #13126635 | C2 | semidirect |
| 3. #13116953 | C2 | semidirect |
| 4. #13116909 | C2 | semidirect |
| 5. #13116792 | C2 | semidirect |
| 6. #13116718 | C2 | semidirect |
| 7. #13116674 | C2 | semidirect |
| 8. C13×#2246 | C2 | semidirect |
| 10. #11719462 | C22 | semidirect |
| 11. C2×C13×D16 | C22 | semidirect |
| 12. C2×C13×D16 | C22 | semidirect |
| 13. C13×#493 | C22 | semidirect |
| 15. #11718821 | C22 | semidirect |
| 16. #11718808 | C22 | semidirect |
| 22. #11718562 | C22 | semidirect |
| 24. #11718361 | C22 | semidirect |
| 25. C4×C13×C16 | C22 | semidirect |
| 26. #11718155 | C22 | semidirect |
| 27. #11718102 | C22 | semidirect |
| 28. #11718100 | C22 | semidirect |
| 29. #11718098 | C22 | semidirect |
| 30. #11718055 | C22 | semidirect |
| 61. Dic104 | D4 | semidirect |
| 62. #88040 | D4 | semidirect |
| 63. D208 | D4 | semidirect |
| 105. #2246 | D13 | semidirect |
| 142. C2×D16 | C2×D13 | semidirect |
| 143. C2×D16 | C2×D13 | semidirect |
| 145. #493 | C2×D13 | semidirect |
| 156. C4×C16 | C2×D13 | semidirect |
| 244. C13 | #33858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13127973 | 2 |
| #13126635 | 2 |
| #13116953 | 2 |
| #13116909 | 2 |
| #13116792 | 2 |
| #13116718 | 2 |
| #13116674 | 2 |
| C13×#2246 | 2 |
| #33858 | 13 |