Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#124 | C2 | semidirect |
| 2. C2×#88196 | C2 | semidirect |
| 4. C4×#6127 | C2 | semidirect |
| 5. #11718886 | C2 | semidirect |
| 6. #11718876 | C2 | semidirect |
| 7. #11718718 | C2 | semidirect |
| 8. #11718715 | C2 | semidirect |
| 9. #11718585 | C2 | semidirect |
| 18. C2×#6107 | C22 | semidirect |
| 20. C2×#6106 | C22 | semidirect |
| 28. C4×D52 | C22 | semidirect |
| 31. C4×Dic26 | C22 | semidirect |
| 32. #88075 | C22 | semidirect |
| 34. C4⋊#1055 | C22 | semidirect |
| 107. C2×#124 | D13 | semidirect |
| 198. C13 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#124 | 2 |
| C2×#88196 | 2 |
| C2×#88186 | 2 |
| C4×#6127 | 2 |
| #11718886 | 2 |
| #11718876 | 2 |
| #11718718 | 2 |
| #11718715 | 2 |
| #11718585 | 2 |
| #3040 | 13 |