Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
400 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 100 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. #13130554 | C2 | semidirect |
| 4. C8×#6118 | C2 | semidirect |
| 5. #13129729 | C2 | semidirect |
| 6. #13129723 | C2 | semidirect |
| 13. C8×Q8×C13 | C4 | semidirect |
| 14. #11718685 | C4 | semidirect |
| 16. #11718499 | C4 | semidirect |
| 21. C8×D52 | C4 | semidirect |
| 23. #11718299 | C4 | semidirect |
| 29. #11718242 | C4 | semidirect |
| 156. C8×Q8 | #261 | semidirect |
| 283. C13 | #8250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13130554 | 2 |
| #13130288 | 2 |
| #13130209 | 2 |
| C8×#6118 | 2 |
| #13129729 | 2 |
| #13129723 | 2 |
| #13123813 | 2 |
| #8250 | 13 |