Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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. C13×#547 | C2 | semidirect |
| 2. C2×#88204 | C2 | semidirect |
| 3. #11719258 | C2 | semidirect |
| 4. #11718899 | C2 | semidirect |
| 5. #11718751 | C2 | semidirect |
| 6. #11718746 | C2 | semidirect |
| 7. #11718709 | C2 | semidirect |
| 8. #11718708 | C2 | semidirect |
| 9. C4×#6105 | C2 | semidirect |
| 10. #11718676 | C2 | semidirect |
| 11. D4×#1055 | C2 | semidirect |
| 72. #6105 | D4 | semidirect |
| 118. #547 | D13 | semidirect |
| 141. C4×C13 | #135 | semidirect |
| 222. C13 | #3284 | semidirect |
| 272. C4 | #88204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#547 | 2 |
| C2×#88204 | 2 |
| #11719258 | 2 |
| #11718899 | 2 |
| #11718751 | 2 |
| #11718746 | 2 |
| #11718709 | 2 |
| #11718708 | 2 |
| C4×#6105 | 2 |
| #11718676 | 2 |
| D4×#1055 | 2 |
| #3284 | 13 |