Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
186 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 55 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×D208 | C2 | semidirect |
| 2. #11718356 | C2 | semidirect |
| 3. C4×D104 | C2 | semidirect |
| 4. C13×C4⋊C16 | C2 | semidirect |
| 5. #11718101 | C2 | semidirect |
| 30. D104 | D4 | semidirect |
| 52. C4⋊C16 | D13 | semidirect |
| 62. C4×C13 | D16 | semidirect |
| 97. C13 | #2206 | semidirect |
| 123. C4 | D208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D208 | 2 |
| #11718356 | 2 |
| C4×D104 | 2 |
| C13×C4⋊C16 | 2 |
| #11718101 | 2 |
| #2206 | 13 |