Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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. C13×#477 | C2 | semidirect |
| 4. #11718754 | C2 | semidirect |
| 5. C4×#6107 | C2 | semidirect |
| 6. #11718548 | C2 | semidirect |
| 7. #11718545 | C2 | semidirect |
| 8. #11718510 | C2 | semidirect |
| 10. #11718469 | C2 | semidirect |
| 11. D13×#103 | C2 | semidirect |
| 91. D52 | Q16 | semidirect |
| 108. #477 | D13 | semidirect |
| 198. C13 | #3299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719435 | 2 |
| Q8×D52 | 2 |
| C13×#477 | 2 |
| #11718754 | 2 |
| C4×#6107 | 2 |
| #11718548 | 2 |
| #11718545 | 2 |
| #11718510 | 2 |
| #11718495 | 2 |
| #11718469 | 2 |
| D13×#103 | 2 |
| #3299 | 13 |