Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 2. C2×#88178 | C2 | semidirect |
| 3. #11718900 | C2 | semidirect |
| 4. C2×C22⋊#1055 | C2 | semidirect |
| 5. #11718712 | C2 | semidirect |
| 6. #11718711 | C2 | semidirect |
| 7. #11718704 | C2 | semidirect |
| 8. #11718702 | C2 | semidirect |
| 9. #11718701 | C2 | semidirect |
| 10. #11718694 | C2 | semidirect |
| 11. #11718657 | C2 | semidirect |
| 25. C2×#6107 | C22 | semidirect |
| 26. C2×#6105 | C22 | semidirect |
| 34. #88075 | C22 | semidirect |
| 35. #88072 | C22 | semidirect |
| 39. #88050 | C22 | semidirect |
| 40. #88050 | C22 | semidirect |
| 41. #88048 | C22 | semidirect |
| 42. #88047 | C22 | semidirect |
| 233. C13 | #3190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#525 | 2 |
| C2×#88178 | 2 |
| #11718900 | 2 |
| C2×C22⋊#1055 | 2 |
| #11718712 | 2 |
| #11718711 | 2 |
| #11718704 | 2 |
| #11718702 | 2 |
| #11718701 | 2 |
| #11718694 | 2 |
| #11718657 | 2 |
| #3190 | 13 |