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. #13125413 | C2 | semidirect |
| 2. D13×#493 | C2 | semidirect |
| 3. #13117085 | C2 | semidirect |
| 4. #13117060 | C2 | semidirect |
| 5. #13117059 | C2 | semidirect |
| 6. #13116869 | C2 | semidirect |
| 7. #13116746 | C2 | semidirect |
| 8. #13116633 | C2 | semidirect |
| 9. C13×#2246 | C2 | semidirect |
| 14. C2×C13×D16 | C22 | semidirect |
| 16. C13×#493 | C22 | semidirect |
| 22. D8×Dic13 | C22 | semidirect |
| 23. C2×#88066 | C22 | semidirect |
| 28. #11718343 | C22 | semidirect |
| 29. C4×C13×C16 | C22 | semidirect |
| 30. #11718154 | C22 | semidirect |
| 31. #11718101 | C22 | semidirect |
| 33. #11718093 | C22 | semidirect |
| 34. C4×#6090 | C22 | semidirect |
| 128. #2246 | D13 | semidirect |
| 168. C4×D13 | D16 | semidirect |
| 179. C2×D16 | C2×D13 | semidirect |
| 186. #493 | 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 |
|---|---|
| #13125413 | 2 |
| D13×#493 | 2 |
| #13117085 | 2 |
| #13117060 | 2 |
| #13117059 | 2 |
| #13116869 | 2 |
| #13116746 | 2 |
| #13116633 | 2 |
| C13×#2246 | 2 |
| #33771 | 13 |