Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
668 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 143 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. #13127974 | C2 | semidirect |
| 2. #13126636 | C2 | semidirect |
| 3. #13117086 | C2 | semidirect |
| 4. #13116957 | C2 | semidirect |
| 5. #13116912 | C2 | semidirect |
| 6. #13116794 | C2 | semidirect |
| 7. #13116674 | C2 | semidirect |
| 8. C13×#2178 | C2 | semidirect |
| 9. #11719474 | C22 | semidirect |
| 12. C13×#443 | C22 | semidirect |
| 13. #11718854 | C22 | semidirect |
| 18. C2×D208 | C22 | semidirect |
| 19. C2×D208 | C22 | semidirect |
| 20. #11718562 | C22 | semidirect |
| 21. #11718558 | C22 | semidirect |
| 24. #11718356 | C22 | semidirect |
| 25. C13×#368 | C22 | semidirect |
| 26. C13×#359 | C22 | semidirect |
| 27. C4×C13×C16 | C22 | semidirect |
| 28. #11718100 | C22 | semidirect |
| 29. #11718087 | C22 | semidirect |
| 30. #11718055 | C22 | semidirect |
| 47. C13×Q32 | D4 | semidirect |
| 48. C13×SD32 | D4 | semidirect |
| 49. C13×D16 | D4 | semidirect |
| 109. #2178 | D13 | semidirect |
| 150. #443 | C2×D13 | semidirect |
| 151. #368 | C2×D13 | semidirect |
| 154. #359 | C2×D13 | semidirect |
| 156. C4×C16 | C2×D13 | semidirect |
| 184. Q32 | D52 | semidirect |
| 186. SD32 | D52 | semidirect |
| 191. D16 | D52 | semidirect |
| 244. C13 | #33858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13127974 | 2 |
| #13126636 | 2 |
| #13117086 | 2 |
| #13116957 | 2 |
| #13116912 | 2 |
| #13116794 | 2 |
| #13116674 | 2 |
| C13×#2178 | 2 |
| #33858 | 13 |