Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
436 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 141 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×#88142 | C2 | semidirect |
| 3. C2×C13×#103 | C2 | semidirect |
| 4. C2×#88075 | C2 | semidirect |
| 6. C2×#88055 | C2 | semidirect |
| 8. #11718456 | C2 | direct (N × H) |
| 23. #88142 | C22 | semidirect |
| 24. C13×#103 | C22 | semidirect |
| 25. #88075 | C22 | semidirect |
| 27. #88055 | C22 | semidirect |
| 92. C2×#103 | D13 | semidirect |
| 128. #103 | C2×D13 | semidirect |
| 132. C2×C13 | #489 | semidirect |
| 167. C13 | C2×#489 | semidirect |
| 213. C2 | #11718456 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88201 | 2 |
| C2×#88142 | 2 |
| C2×C13×#103 | 2 |
| C2×#88075 | 2 |
| C2×#88061 | 2 |
| C2×#88055 | 2 |
| C2×#88049 | 2 |
| #11718456 | 2 |
| C2×#489 | 13 |