Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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. C13×#519 | C2 | semidirect |
| 4. #11718886 | C2 | semidirect |
| 5. #11718687 | C2 | semidirect |
| 6. C4×#6106 | C2 | semidirect |
| 8. #11718659 | C2 | semidirect |
| 9. #11718658 | C2 | semidirect |
| 13. C4×Q8×C13 | C22 | semidirect |
| 17. C2×#6106 | C4 | semidirect |
| 26. #88075 | C22 | semidirect |
| 28. #88048 | C22 | semidirect |
| 29. #88047 | C22 | semidirect |
| 30. #88043 | C22 | semidirect |
| 31. C4×#1055 | C22 | semidirect |
| 35. C2×Q8×C13 | C2×C4 | semidirect |
| 53. #6106 | C2×C4 | semidirect |
| 54. #6106 | C2×C4 | semidirect |
| 59. C2×#1055 | C2×C4 | semidirect |
| 88. #519 | D13 | semidirect |
| 117. C4×Q8 | C2×D13 | semidirect |
| 138. C2×Q8 | C4×D13 | semidirect |
| 166. C13 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#519 | 2 |
| C22×#6106 | 2 |
| #11719226 | 2 |
| #11718886 | 2 |
| #11718687 | 2 |
| C4×#6106 | 2 |
| #11718662 | 2 |
| #11718659 | 2 |
| #11718658 | 2 |
| #2949 | 13 |