Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 2. C13×#462 | C2 | semidirect |
| 4. #11718739 | C2 | semidirect |
| 5. Q8⋊#1055 | C2 | semidirect |
| 7. #11718074 | C2 | semidirect |
| 65. D52 | Q16 | semidirect |
| 78. #462 | D13 | semidirect |
| 142. C13 | #1649 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D52 | 2 |
| C13×#462 | 2 |
| #11718748 | 2 |
| #11718739 | 2 |
| Q8⋊#1055 | 2 |
| #11718075 | 2 |
| #11718074 | 2 |
| #1649 | 13 |