Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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. #11719503 | C2 | semidirect |
| 3. #11719226 | C2 | semidirect |
| 4. C13×#418 | C2 | semidirect |
| 5. #11718792 | C2 | semidirect |
| 6. #11718783 | C2 | semidirect |
| 7. #11718659 | C2 | semidirect |
| 8. #11718446 | C2 | semidirect |
| 9. #11718417 | C2 | semidirect |
| 16. D4×Dic13 | C22 | semidirect |
| 17. C2×#6104 | C4 | semidirect |
| 23. #88147 | C22 | semidirect |
| 26. C13×#102 | C22 | semidirect |
| 27. #88061 | C22 | semidirect |
| 28. #88055 | C22 | semidirect |
| 29. C8×Dic13 | C22 | semidirect |
| 30. #88048 | C22 | semidirect |
| 31. #88047 | C22 | semidirect |
| 36. C2×D4×C13 | C2×C4 | semidirect |
| 42. C2×D52 | C2×C4 | semidirect |
| 53. #6104 | C2×C4 | semidirect |
| 54. #6104 | C2×C4 | semidirect |
| 60. C2×#1055 | C2×C4 | semidirect |
| 96. #418 | D13 | semidirect |
| 132. #102 | C2×D13 | semidirect |
| 148. C2×D4 | C4×D13 | semidirect |
| 171. C13 | #2948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719503 | 2 |
| C22×#6104 | 2 |
| #11719226 | 2 |
| C13×#418 | 2 |
| #11718792 | 2 |
| #11718783 | 2 |
| #11718659 | 2 |
| #11718446 | 2 |
| #11718417 | 2 |
| #2948 | 13 |