Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
730 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 147 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. #13125416 | C2 | semidirect |
| 2. D13×#493 | C2 | semidirect |
| 3. #13117086 | C2 | semidirect |
| 4. #13117085 | C2 | semidirect |
| 5. #13117061 | C2 | semidirect |
| 6. #13116870 | C2 | semidirect |
| 7. #13116749 | C2 | semidirect |
| 8. #13116633 | C2 | semidirect |
| 9. C13×#2240 | C2 | semidirect |
| 14. C13×#500 | C22 | semidirect |
| 18. C2×#88066 | C22 | semidirect |
| 21. C2×D208 | C22 | semidirect |
| 25. #11718533 | C22 | semidirect |
| 27. #11718356 | C22 | semidirect |
| 29. C13×#357 | C22 | semidirect |
| 30. C4×C13×C16 | C22 | semidirect |
| 32. #11718093 | C22 | semidirect |
| 33. #11718083 | C22 | semidirect |
| 34. C4×#6090 | C22 | semidirect |
| 130. #2240 | D13 | semidirect |
| 169. C4×D13 | D16 | semidirect |
| 180. #500 | C2×D13 | semidirect |
| 195. #357 | C2×D13 | semidirect |
| 198. C4×C16 | C2×D13 | semidirect |
| 317. C13 | #33771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13125416 | 2 |
| D13×#493 | 2 |
| #13117086 | 2 |
| #13117085 | 2 |
| #13117061 | 2 |
| #13116870 | 2 |
| #13116749 | 2 |
| #13116633 | 2 |
| C13×#2240 | 2 |
| #33771 | 13 |