Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
528 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 160 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. #11719623 | C2 | semidirect |
| 3. #11719138 | C2 | semidirect |
| 4. #11719102 | C2 | semidirect |
| 5. D8×#261 | C2 | semidirect |
| 6. #11719092 | C2 | semidirect |
| 7. #11719089 | C2 | semidirect |
| 11. D4×#261 | C22 | semidirect |
| 15. C2×C13×D8 | C4 | semidirect |
| 16. C2×#6104 | C4 | semidirect |
| 17. D8×D13 | C4 | semidirect |
| 18. D8×D13 | C4 | semidirect |
| 21. C2×D104 | C4 | semidirect |
| 23. #88115 | C22 | semidirect |
| 24. #88102 | C22 | semidirect |
| 25. #88101 | C22 | semidirect |
| 26. #88100 | C22 | semidirect |
| 27. C8×#261 | C22 | semidirect |
| 30. C2×D4×C13 | C2×C4 | semidirect |
| 34. D4×D13 | C2×C4 | semidirect |
| 36. C2×D52 | C2×C4 | semidirect |
| 48. C13×D8 | C2×C4 | semidirect |
| 49. C13×D8 | C2×C4 | semidirect |
| 50. C2×C8×C13 | C2×C4 | semidirect |
| 51. #6104 | C2×C4 | semidirect |
| 52. #6104 | C2×C4 | semidirect |
| 53. C2×#1055 | C2×C4 | semidirect |
| 54. D104 | C2×C4 | semidirect |
| 55. D104 | C2×C4 | semidirect |
| 56. C8×D13 | C2×C4 | semidirect |
| 57. C8×D13 | C2×C4 | semidirect |
| 117. C2×D8 | #261 | semidirect |
| 143. C2×D4 | C2×#261 | semidirect |
| 150. D8 | C2×#261 | semidirect |
| 151. D8 | C2×#261 | semidirect |
| 160. C2×C8 | C2×#261 | semidirect |
| 168. C13 | #2948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719623 | 2 |
| C2×D8×D13 | 2 |
| #11719138 | 2 |
| #11719102 | 2 |
| D8×#261 | 2 |
| #11719092 | 2 |
| #11719089 | 2 |
| #2948 | 13 |