Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×C13×Q16 | C2 | semidirect |
| 2. #11719521 | C2 | semidirect |
| 3. C2×#88196 | C2 | semidirect |
| 5. #11718852 | C2 | semidirect |
| 6. #11718851 | C2 | semidirect |
| 7. #11718842 | C2 | semidirect |
| 8. #11718762 | C2 | semidirect |
| 84. C22×Q16 | D13 | semidirect |
| 155. C13 | #3156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×Q16 | 2 |
| #11719521 | 2 |
| C2×#88196 | 2 |
| C2×#88158 | 2 |
| #11718852 | 2 |
| #11718851 | 2 |
| #11718842 | 2 |
| #11718762 | 2 |
| #3156 | 13 |