Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
568 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 161 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. C2×C4×Dic26 | C2 | semidirect |
| 4. C4×C22⋊Dic13 | C2 | semidirect |
| 5. #11718643 | C2 | semidirect |
| 6. #11718614 | C2 | semidirect |
| 7. #11718608 | C2 | semidirect |
| 8. #11718593 | C2 | semidirect |
| 146. C13 | #2398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C13 | 2 |
| C2×C4×Dic26 | 2 |
| #11718883 | 2 |
| C4×C22⋊Dic13 | 2 |
| #11718643 | 2 |
| #11718614 | 2 |
| #11718608 | 2 |
| #11718593 | 2 |
| #2398 | 13 |