Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#88186 | C2 | semidirect |
| 3. #11719182 | C2 | semidirect |
| 4. #11718737 | C2 | semidirect |
| 5. #11718735 | C2 | semidirect |
| 6. #11718734 | C2 | semidirect |
| 7. C4×#6099 | C2 | semidirect |
| 15. C2×#6105 | C22 | semidirect |
| 17. C2×#6104 | C22 | semidirect |
| 20. #88129 | C22 | semidirect |
| 21. #88128 | C22 | semidirect |
| 23. #88123 | C22 | semidirect |
| 24. #88043 | C22 | semidirect |
| 25. C4×#1055 | C22 | semidirect |
| 48. #6099 | D4 | semidirect |
| 72. #1055 | C2×D4 | semidirect |
| 75. C2×#127 | D13 | semidirect |
| 90. C4×C13 | AGL(1,ℤ/8) | semidirect |
| 140. C13 | #3151 | semidirect |
| 173. C4 | #88186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#127 | 2 |
| C2×#88186 | 2 |
| #11719182 | 2 |
| #11718737 | 2 |
| #11718735 | 2 |
| #11718734 | 2 |
| C4×#6099 | 2 |
| #3151 | 13 |