Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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×Dic26 | C2 | semidirect |
| 3. #11718736 | C2 | semidirect |
| 4. #11718731 | C2 | semidirect |
| 5. D4⋊#1055 | C2 | semidirect |
| 6. #11718078 | C2 | semidirect |
| 7. #11718076 | C2 | semidirect |
| 60. D4×C13 | SD16 | semidirect |
| 75. Dic26 | D8 | semidirect |
| 150. C13 | #1627 | semidirect |
| 164. D4 | #6105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic26 | 2 |
| C13×#459 | 2 |
| #11718736 | 2 |
| #11718731 | 2 |
| D4⋊#1055 | 2 |
| #11718078 | 2 |
| #11718076 | 2 |
| #1627 | 13 |