Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
266 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 70 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. #11719129 | C2 | semidirect |
| 3. C4×#6122 | C2 | semidirect |
| 4. Q8⋊#1057 | C2 | semidirect |
| 5. D4⋊#1057 | C2 | semidirect |
| 56. Q8×C13 | M16 | semidirect |
| 59. D4×C13 | M16 | semidirect |
| 154. C13 | #1489 | semidirect |
| 158. Q8 | #6122 | semidirect |
| 161. D4 | #6122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic13 | 2 |
| #11719129 | 2 |
| C4×#6122 | 2 |
| Q8⋊#1057 | 2 |
| D4⋊#1057 | 2 |
| #1489 | 13 |