Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 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×C13×#127 | C2 | semidirect |
| 2. #11719184 | C2 | semidirect |
| 3. #11718879 | C2 | semidirect |
| 4. #11718878 | C2 | semidirect |
| 5. #11718736 | C2 | semidirect |
| 6. #11718735 | C2 | semidirect |
| 7. #11718733 | C2 | semidirect |
| 8. #11718732 | C2 | semidirect |
| 9. #11718587 | C2 | semidirect |
| 18. C2×#6105 | C22 | semidirect |
| 19. C2×#6104 | C22 | semidirect |
| 25. #88129 | C22 | semidirect |
| 26. C4×D52 | C22 | semidirect |
| 28. #88124 | C22 | semidirect |
| 29. C4×Dic26 | C22 | semidirect |
| 30. #88072 | C22 | semidirect |
| 31. #88072 | C22 | semidirect |
| 33. C4⋊#1055 | C22 | semidirect |
| 34. #88043 | C22 | semidirect |
| 102. C2×#127 | D13 | semidirect |
| 198. C13 | #3217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#127 | 2 |
| #11719184 | 2 |
| #11718879 | 2 |
| #11718878 | 2 |
| #11718736 | 2 |
| #11718735 | 2 |
| #11718733 | 2 |
| #11718732 | 2 |
| #11718587 | 2 |
| #3217 | 13 |