Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
448 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11719289 | C2 | semidirect |
| 3. C4×C13×SD16 | C2 | semidirect |
| 4. #11718830 | C2 | semidirect |
| 5. #11718688 | C2 | semidirect |
| 6. #11718668 | C2 | semidirect |
| 7. #11718527 | C2 | semidirect |
| 8. #11718473 | C2 | semidirect |
| 9. #11718431 | C2 | semidirect |
| 10. #11718355 | C2 | semidirect |
| 11. #11718349 | C2 | semidirect |
| 15. C4×Q8×C13 | C22 | semidirect |
| 17. #88200 | C22 | semidirect |
| 18. C2×#6106 | C22 | semidirect |
| 20. C2×#6094 | C22 | semidirect |
| 23. #88146 | C22 | semidirect |
| 28. #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. #88047 | C22 | semidirect |
| 40. C4⋊#1055 | C22 | semidirect |
| 118. C4×SD16 | D13 | semidirect |
| 155. C4×Q8 | C2×D13 | semidirect |
| 160. #106 | C2×D13 | semidirect |
| 162. #103 | C2×D13 | semidirect |
| 169. C4×C8 | C2×D13 | semidirect |
| 212. C13 | #3324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719289 | 2 |
| D4×D52 | 2 |
| C4×C13×SD16 | 2 |
| #11718830 | 2 |
| #11718688 | 2 |
| #11718668 | 2 |
| #11718527 | 2 |
| #11718473 | 2 |
| #11718431 | 2 |
| #11718355 | 2 |
| #11718349 | 2 |
| #3324 | 13 |