Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11719258 | C2 | semidirect |
| 2. #11719248 | C2 | semidirect |
| 3. C4×C13×D8 | C2 | semidirect |
| 4. #11718811 | C2 | semidirect |
| 5. #11718676 | C2 | semidirect |
| 6. #11718669 | C2 | semidirect |
| 7. #11718552 | C2 | semidirect |
| 8. #11718446 | C2 | semidirect |
| 9. #11718425 | C2 | semidirect |
| 10. #11718355 | C2 | semidirect |
| 11. #11718340 | C2 | semidirect |
| 81. D4×C13 | #41 | semidirect |
| 115. C4×D8 | D13 | semidirect |
| 203. C13 | #3366 | semidirect |
| 218. D4 | #6127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719258 | 2 |
| #11719248 | 2 |
| C4×C13×D8 | 2 |
| #11718811 | 2 |
| #11718676 | 2 |
| #11718669 | 2 |
| #11718552 | 2 |
| #11718446 | 2 |
| #11718425 | 2 |
| #11718355 | 2 |
| #11718340 | 2 |
| #3366 | 13 |