Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
456 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 3. #13130594 | C2 | semidirect |
| 4. #13130593 | C2 | semidirect |
| 5. #13129926 | C2 | semidirect |
| 6. #13129923 | C2 | semidirect |
| 8. C22×#6122 | C4 | semidirect |
| 11. #11719169 | C4 | semidirect |
| 18. #11719067 | C4 | semidirect |
| 22. #11719062 | C4 | semidirect |
| 25. #11718306 | C4 | semidirect |
| 28. #11718237 | C4 | semidirect |
| 29. C13×AΣL(1,𝔽16) | C4 | semidirect |
| 30. #11718128 | C4 | semidirect |
| 31. #11718068 | C4 | semidirect |
| 32. #11718064 | C4 | semidirect |
| 217. AΣL(1,𝔽16) | #261 | semidirect |
| 360. C13 | #12624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13131555 | 2 |
| #13131088 | 2 |
| #13130594 | 2 |
| #13130593 | 2 |
| #13129926 | 2 |
| #13129923 | 2 |
| #13116474 | 2 |
| #12624 | 13 |