Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 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. D4×Q8×C13 | C2 | semidirect |
| 2. C2×#88196 | C2 | semidirect |
| 4. #11718888 | C2 | semidirect |
| 5. #11718751 | C2 | semidirect |
| 6. #11718746 | C2 | semidirect |
| 7. #11718710 | C2 | semidirect |
| 8. #11718708 | C2 | semidirect |
| 9. C4×#6107 | C2 | semidirect |
| 10. #11718688 | C2 | semidirect |
| 11. #11718673 | C2 | semidirect |
| 70. #6107 | D4 | semidirect |
| 117. D4×Q8 | D13 | semidirect |
| 138. C4×C13 | #137 | semidirect |
| 218. C13 | #3278 | semidirect |
| 265. C4 | #88196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Q8×C13 | 2 |
| C2×#88196 | 2 |
| #11719258 | 2 |
| #11718888 | 2 |
| #11718751 | 2 |
| #11718746 | 2 |
| #11718710 | 2 |
| #11718708 | 2 |
| C4×#6107 | 2 |
| #11718688 | 2 |
| #11718673 | 2 |
| #3278 | 13 |