Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
992 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 221 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. C2×#88063 | C2 | semidirect |
| 6. D13×#100 | C2 | direct (N × H) |
| 17. C2×C13×M16 | C22 | semidirect |
| 18. C2×#6099 | C22 | semidirect |
| 20. M16×D13 | C22 | semidirect |
| 23. C13×#100 | C22 | semidirect |
| 24. #88073 | C22 | semidirect |
| 25. #88063 | C22 | semidirect |
| 57. C13×M16 | C23 | semidirect |
| 60. #6099 | C23 | semidirect |
| 108. C2×#100 | D13 | direct (N × H) |
| 126. C2×D13 | #100 | direct (N × H) |
| 146. C2×M16 | C2×D13 | semidirect |
| 150. #100 | C2×D13 | direct (N × H) |
| 154. C2×C13 | C2×#100 | semidirect |
| 158. D13 | C2×#100 | direct (N × H) |
| 193. M16 | C22×D13 | semidirect |
| 197. C13 | C22×#100 | semidirect |
| 265. 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×M16×D13 | 2 |
| C2×C13×#100 | 2 |
| C2×#88073 | 2 |
| C2×#88063 | 2 |
| D13×#100 | 2 |
| C22×#100 | 13 |