Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11719184 | C2 | semidirect |
| 2. C2×#88129 | C2 | semidirect |
| 3. C13×#431 | C2 | semidirect |
| 4. #11718506 | C2 | semidirect |
| 5. #11718505 | C2 | semidirect |
| 6. #11718400 | C2 | semidirect |
| 7. #11718399 | C2 | semidirect |
| 9. #11718392 | C2 | semidirect |
| 10. #11718358 | C2 | semidirect |
| 11. #11718357 | C2 | semidirect |
| 21. C2×Dic52 | C22 | semidirect |
| 24. C2×#6095 | C22 | semidirect |
| 30. #88129 | C22 | semidirect |
| 31. C4×D52 | C22 | semidirect |
| 33. #88124 | C22 | semidirect |
| 34. C4×Dic26 | C22 | semidirect |
| 35. C13×C4⋊C8 | C22 | semidirect |
| 38. C4×C8×C13 | C22 | semidirect |
| 41. #88056 | C22 | semidirect |
| 42. #88056 | C22 | semidirect |
| 127. #431 | D13 | semidirect |
| 172. C4⋊C8 | C2×D13 | semidirect |
| 179. C4×C8 | C2×D13 | semidirect |
| 227. C13 | #3211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719184 | 2 |
| C2×#88129 | 2 |
| C13×#431 | 2 |
| #11718506 | 2 |
| #11718505 | 2 |
| #11718400 | 2 |
| #11718399 | 2 |
| #11718393 | 2 |
| #11718392 | 2 |
| #11718358 | 2 |
| #11718357 | 2 |
| #3211 | 13 |