Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
994 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 167 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. #13125573 | C2 | semidirect |
| 3. #13125287 | C2 | semidirect |
| 4. #13125283 | C2 | semidirect |
| 5. #13114504 | C2 | semidirect |
| 6. #13114502 | C2 | semidirect |
| 7. #13114463 | C2 | semidirect |
| 8. #13114450 | C2 | semidirect |
| 9. #13114424 | C2 | semidirect |
| 10. #13113140 | C2 | semidirect |
| 11. C13×#1715 | C2 | semidirect |
| 17. C13×#498 | C22 | semidirect |
| 20. C13×#486 | C22 | semidirect |
| 23. #11718749 | C22 | semidirect |
| 25. #11718740 | C22 | semidirect |
| 29. #11718734 | C22 | semidirect |
| 35. #11718356 | C22 | semidirect |
| 36. #11718355 | C22 | semidirect |
| 40. C13×#322 | C22 | semidirect |
| 41. #11718046 | C22 | semidirect |
| 42. C8×#1055 | C22 | semidirect |
| 146. #1715 | D13 | semidirect |
| 183. C8×C13 | AGL(1,ℤ/8) | semidirect |
| 185. #1055 | AGL(1,ℤ/8) | semidirect |
| 192. #498 | C2×D13 | semidirect |
| 207. #486 | C2×D13 | semidirect |
| 215. #322 | C2×D13 | semidirect |
| 338. C13 | #19745 | semidirect |
| 374. C8 | #88168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13125575 | 2 |
| #13125573 | 2 |
| #13125287 | 2 |
| #13125283 | 2 |
| #13114504 | 2 |
| #13114502 | 2 |
| #13114463 | 2 |
| #13114450 | 2 |
| #13114424 | 2 |
| #13113140 | 2 |
| C13×#1715 | 2 |
| #19745 | 13 |