Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
356 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #11718777 | C2 | semidirect |
| 4. C2×#88058 | C2 | semidirect |
| 5. #11718511 | C2 | semidirect |
| 6. #11718383 | C2 | semidirect |
| 7. C4×Dic52 | C2 | semidirect |
| 8. #11718343 | C2 | semidirect |
| 51. D4×C13 | Q16 | semidirect |
| 132. C13 | #3338 | semidirect |
| 137. D4 | Dic52 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719248 | 2 |
| C8×D4×C13 | 2 |
| #11718777 | 2 |
| C2×#88058 | 2 |
| #11718511 | 2 |
| #11718383 | 2 |
| C4×Dic52 | 2 |
| #11718343 | 2 |
| #3338 | 13 |