Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. #11719432 | C2 | semidirect |
| 2. C13×#500 | C2 | semidirect |
| 3. #11718748 | C2 | semidirect |
| 4. #11718551 | C2 | semidirect |
| 5. #11718535 | C2 | semidirect |
| 8. C8×Dic26 | C2 | semidirect |
| 48. D104 | Q8 | semidirect |
| 60. D52 | C2×Q8 | semidirect |
| 64. Dic26 | D8 | semidirect |
| 66. C8×C13 | C2×Q8 | semidirect |
| 70. #500 | D13 | semidirect |
| 132. C13 | Q8×D8 | semidirect |
| 150. C8 | Q8×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719432 | 2 |
| C13×#500 | 2 |
| #11718748 | 2 |
| #11718551 | 2 |
| #11718535 | 2 |
| #11718533 | 2 |
| C4×D104 | 2 |
| C8×Dic26 | 2 |
| Q8×D8 | 13 |