Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
226 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 53 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. C2×Q16×D13 | C2 | semidirect |
| 2. C2×C13×SD32 | C2 | semidirect |
| 4. C2×#88067 | C2 | semidirect |
| 5. #11718156 | C2 | semidirect |
| 6. #11718099 | C2 | semidirect |
| 7. #11718095 | C2 | semidirect |
| 33. C13×Q16 | D4 | semidirect |
| 42. Dic52 | D4 | semidirect |
| 71. C2×SD32 | D13 | semidirect |
| 82. C2×D13 | SD32 | semidirect |
| 122. Q16 | C22⋊D13 | semidirect |
| 133. C13 | #2185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D13 | 2 |
| C2×C13×SD32 | 2 |
| #11718818 | 2 |
| C2×#88067 | 2 |
| #11718156 | 2 |
| #11718099 | 2 |
| #11718095 | 2 |
| #2185 | 13 |