Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 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 |
|---|---|---|
| 1. #11719284 | C2 | semidirect |
| 3. C4×C13×SD16 | C2 | semidirect |
| 4. #11718830 | C2 | semidirect |
| 5. #11718688 | C2 | semidirect |
| 6. #11718669 | C2 | semidirect |
| 7. #11718524 | C2 | semidirect |
| 8. #11718468 | C2 | semidirect |
| 9. D13×#102 | C2 | semidirect |
| 10. #11718355 | C2 | semidirect |
| 11. C8×D52 | C2 | semidirect |
| 15. C4×Q8×C13 | C22 | semidirect |
| 17. #88200 | C22 | semidirect |
| 18. C2×#6106 | C22 | semidirect |
| 20. C2×C8×D13 | C22 | semidirect |
| 23. C4⋊C4×D13 | C22 | semidirect |
| 29. #88123 | C22 | semidirect |
| 30. C13×#106 | C22 | semidirect |
| 31. C13×#103 | C22 | semidirect |
| 33. C4×C8×C13 | C22 | semidirect |
| 35. #88061 | C22 | semidirect |
| 36. #88061 | C22 | semidirect |
| 37. #88060 | C22 | semidirect |
| 38. #88049 | C22 | semidirect |
| 39. #88048 | C22 | semidirect |
| 40. C4⋊#1055 | C22 | semidirect |
| 103. D52 | SD16 | semidirect |
| 119. C4×SD16 | D13 | semidirect |
| 155. C4×Q8 | C2×D13 | semidirect |
| 161. #106 | C2×D13 | semidirect |
| 163. #103 | C2×D13 | semidirect |
| 170. C4×C8 | C2×D13 | semidirect |
| 213. C13 | #3295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719284 | 2 |
| D4×D52 | 2 |
| C4×C13×SD16 | 2 |
| #11718830 | 2 |
| #11718688 | 2 |
| #11718669 | 2 |
| #11718524 | 2 |
| #11718468 | 2 |
| D13×#102 | 2 |
| #11718355 | 2 |
| C8×D52 | 2 |
| #3295 | 13 |