Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
564 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 123 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. #13125575 | C2 | semidirect |
| 2. #13123741 | C2 | semidirect |
| 3. #13117052 | C2 | semidirect |
| 4. #13117004 | C2 | semidirect |
| 5. #13116913 | C2 | semidirect |
| 6. #13116912 | C2 | semidirect |
| 7. #13116783 | C2 | semidirect |
| 8. #13116733 | C2 | semidirect |
| 9. #13116731 | C2 | semidirect |
| 10. #13116647 | C2 | semidirect |
| 11. C13×#2230 | C2 | semidirect |
| 15. C13×#498 | C22 | semidirect |
| 25. #11718530 | C22 | semidirect |
| 31. #11718356 | C22 | semidirect |
| 33. C13×#365 | C22 | semidirect |
| 34. C13×#364 | C22 | semidirect |
| 36. #11718108 | C22 | semidirect |
| 38. #11718104 | C22 | semidirect |
| 39. #11718087 | C22 | semidirect |
| 41. #11718079 | C22 | semidirect |
| 42. #11718055 | C22 | semidirect |
| 114. C13×Q16 | #41 | semidirect |
| 116. C13×D8 | #41 | semidirect |
| 138. Dic52 | #41 | semidirect |
| 143. D104 | #41 | semidirect |
| 161. #2230 | D13 | semidirect |
| 214. #498 | C2×D13 | semidirect |
| 231. #365 | C2×D13 | semidirect |
| 233. #364 | C2×D13 | semidirect |
| 335. Q16 | #6131 | semidirect |
| 346. D8 | #6131 | semidirect |
| 376. C13 | #33688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13125575 | 2 |
| #13123741 | 2 |
| #13117052 | 2 |
| #13117004 | 2 |
| #13116913 | 2 |
| #13116912 | 2 |
| #13116783 | 2 |
| #13116733 | 2 |
| #13116731 | 2 |
| #13116647 | 2 |
| C13×#2230 | 2 |
| #33688 | 13 |