Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
474 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 95 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×SD16 | C2 | semidirect |
| 2. C22×#6106 | C2 | semidirect |
| 4. #11718891 | C2 | semidirect |
| 5. C2×#88072 | C2 | semidirect |
| 6. C2×#88061 | C2 | semidirect |
| 7. #11718142 | C2 | semidirect |
| 34. C2×Q8×C13 | D4 | semidirect |
| 57. C2×C8×C13 | D4 | semidirect |
| 65. C2×#1055 | D4 | semidirect |
| 100. C2×Dic13 | SD16 | semidirect |
| 108. C22×SD16 | D13 | semidirect |
| 169. C2×Q8 | C22⋊D13 | semidirect |
| 196. C2×C8 | C22⋊D13 | semidirect |
| 201. C13 | #2014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×SD16 | 2 |
| C22×#6106 | 2 |
| C2×#88194 | 2 |
| #11718891 | 2 |
| C2×#88072 | 2 |
| C2×#88061 | 2 |
| #11718142 | 2 |
| #2014 | 13 |