Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
166 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 56 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. #11719158 | C2 | semidirect |
| 4. Q8⋊#1057 | C2 | semidirect |
| 5. #11718255 | C2 | semidirect |
| 6. C8×#1057 | C2 | semidirect |
| 59. #1057 | SD16 | semidirect |
| 61. #1055 | M16 | semidirect |
| 118. C13 | #1590 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719158 | 2 |
| #11719076 | 2 |
| #11718449 | 2 |
| Q8⋊#1057 | 2 |
| #11718255 | 2 |
| C8×#1057 | 2 |
| #11718243 | 2 |
| #1590 | 13 |