Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
390 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D13 | C2 | semidirect |
| 3. C2×C13×#100 | C2 | semidirect |
| 4. C2×#88073 | C2 | semidirect |
| 5. #11718787 | C2 | semidirect |
| 6. #11718146 | C2 | semidirect |
| 7. #11718146 | C2 | semidirect |
| 54. C13×M16 | D4 | semidirect |
| 64. #6099 | D4 | semidirect |
| 115. C2×#100 | D13 | semidirect |
| 136. C2×D13 | #100 | semidirect |
| 203. M16 | C22⋊D13 | semidirect |
| 213. C13 | #1900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88192 | 2 |
| C2×M16×D13 | 2 |
| C2×C13×#100 | 2 |
| C2×#88073 | 2 |
| #11718787 | 2 |
| #11718146 | 2 |
| #1900 | 13 |