Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
618 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 131 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. #13125483 | C2 | semidirect |
| 2. #13125318 | C2 | semidirect |
| 3. #13117085 | C2 | semidirect |
| 4. #13117078 | C2 | semidirect |
| 5. #13117067 | C2 | semidirect |
| 6. #13116893 | C2 | semidirect |
| 7. #13116869 | C2 | semidirect |
| 8. #13116758 | C2 | semidirect |
| 9. #13116746 | C2 | semidirect |
| 10. #13116644 | C2 | semidirect |
| 11. C13×#2250 | C2 | semidirect |
| 17. C2×C13×SD32 | C22 | semidirect |
| 20. C13×#493 | C22 | semidirect |
| 27. D8×Dic13 | C22 | semidirect |
| 29. C2×#88066 | C22 | semidirect |
| 34. #11718344 | C22 | semidirect |
| 35. C13×#346 | C22 | semidirect |
| 36. #11718156 | C22 | semidirect |
| 39. #11718101 | C22 | semidirect |
| 41. #11718093 | C22 | semidirect |
| 42. C4×#6090 | C22 | semidirect |
| 142. #2250 | D13 | semidirect |
| 193. C2×SD32 | C2×D13 | semidirect |
| 204. #493 | C2×D13 | semidirect |
| 217. #346 | C2×D13 | semidirect |
| 342. C13 | #33786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13125483 | 2 |
| #13125318 | 2 |
| #13117085 | 2 |
| #13117078 | 2 |
| #13117067 | 2 |
| #13116893 | 2 |
| #13116869 | 2 |
| #13116758 | 2 |
| #13116746 | 2 |
| #13116644 | 2 |
| C13×#2250 | 2 |
| #33786 | 13 |