Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
992 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 210 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×D13⋊M16 | C2 | semidirect |
| 3. C2×#88121 | C2 | semidirect |
| 4. D13⋊#100 | C2 | direct (N × H) |
| 15. C2×#6122 | C22 | semidirect |
| 17. D13⋊M16 | C22 | semidirect |
| 20. #88121 | C22 | semidirect |
| 51. #6122 | C23 | semidirect |
| 113. C2×D13 | #100 | semidirect |
| 138. C2×C13 | C2×#100 | semidirect |
| 142. D13 | C2×#100 | semidirect |
| 177. C13 | C22×#100 | semidirect |
| 243. C2 | D13⋊#100 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D13 | 2 |
| C2×D13⋊M16 | 2 |
| C2×#88121 | 2 |
| D13⋊#100 | 2 |
| C22×#100 | 13 |