Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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×#117 | C2 | semidirect |
| 3. C2×C22⋊#1055 | C2 | semidirect |
| 4. #11718664 | C2 | semidirect |
| 5. #11718663 | C2 | semidirect |
| 6. #11718659 | C2 | semidirect |
| 7. #11718657 | C2 | semidirect |
| 8. #11718632 | C2 | semidirect |
| 9. #11718631 | C2 | semidirect |
| 10. #11718629 | C2 | semidirect |
| 11. #11718628 | C2 | semidirect |
| 35. #88050 | C22 | semidirect |
| 36. #88050 | C22 | semidirect |
| 37. #88049 | C22 | semidirect |
| 38. #88049 | C22 | semidirect |
| 39. #88048 | C22 | semidirect |
| 40. #88048 | C22 | semidirect |
| 41. #88047 | C22 | semidirect |
| 42. #88047 | C22 | semidirect |
| 115. C2×#117 | D13 | semidirect |
| 224. C13 | #3091 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#117 | 2 |
| #11719496 | 2 |
| C2×C22⋊#1055 | 2 |
| #11718664 | 2 |
| #11718663 | 2 |
| #11718659 | 2 |
| #11718657 | 2 |
| #11718632 | 2 |
| #11718631 | 2 |
| #11718629 | 2 |
| #11718628 | 2 |
| #3091 | 13 |