Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
488 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 133 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×#88186 | C2 | semidirect |
| 2. C22×#6104 | C2 | semidirect |
| 3. C2×#88162 | C2 | semidirect |
| 4. C2×#88161 | C2 | semidirect |
| 5. C2×C13×#100 | C2 | semidirect |
| 6. C2×#88063 | C2 | semidirect |
| 7. C2×#88062 | C2 | semidirect |
| 8. #11718410 | C2 | direct (N × H) |
| 16. #88186 | C22 | semidirect |
| 21. C2×#6104 | C22 | semidirect |
| 25. #88162 | C22 | semidirect |
| 27. #88161 | C22 | semidirect |
| 32. C13×#100 | C22 | semidirect |
| 33. #88063 | C22 | semidirect |
| 34. #88062 | C22 | semidirect |
| 125. C2×#100 | D13 | semidirect |
| 170. #100 | C2×D13 | semidirect |
| 174. C2×C13 | #472 | semidirect |
| 222. C13 | C2×#472 | semidirect |
| 285. C2 | #11718410 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88186 | 2 |
| C22×#6104 | 2 |
| C2×#88162 | 2 |
| C2×#88161 | 2 |
| C2×C13×#100 | 2 |
| C2×#88063 | 2 |
| C2×#88062 | 2 |
| #11718410 | 2 |
| C2×#472 | 13 |