Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×C13×SD16 | C2 | semidirect |
| 2. C2×#88201 | C2 | semidirect |
| 3. C2×D4×Dic13 | C2 | semidirect |
| 5. C2×#88075 | C2 | semidirect |
| 6. #11718826 | C2 | direct (N × H) |
| 7. C2×#88061 | C2 | semidirect |
| 8. C2×#88054 | C2 | semidirect |
| 14. C2×C13×SD16 | C22 | semidirect |
| 18. #88201 | C22 | semidirect |
| 20. D4×Dic13 | C22 | semidirect |
| 28. #88075 | C22 | semidirect |
| 29. #88061 | C22 | semidirect |
| 30. #88054 | C22 | semidirect |
| 99. C22×SD16 | D13 | semidirect |
| 131. C2×SD16 | C2×D13 | semidirect |
| 149. C2×C13 | #463 | semidirect |
| 188. C13 | C2×#463 | semidirect |
| 243. C2 | #11718826 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×SD16 | 2 |
| C2×#88201 | 2 |
| C2×D4×Dic13 | 2 |
| C22×#6104 | 2 |
| C2×#88075 | 2 |
| #11718826 | 2 |
| C2×#88061 | 2 |
| C2×#88054 | 2 |
| C2×#463 | 13 |