Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#88257 | C2 | semidirect |
| 2. #11719527 | C2 | semidirect |
| 3. #11719453 | C2 | semidirect |
| 4. #11719231 | C2 | semidirect |
| 5. C13×#421 | C2 | semidirect |
| 6. C2×#88064 | C2 | semidirect |
| 7. #11718666 | C2 | semidirect |
| 8. #11718488 | C2 | semidirect |
| 9. #11718487 | C2 | semidirect |
| 25. #88205 | C22 | semidirect |
| 27. #88203 | C22 | semidirect |
| 32. #88163 | C22 | semidirect |
| 34. #88162 | C22 | semidirect |
| 38. #88129 | C22 | semidirect |
| 39. #88123 | C22 | semidirect |
| 40. C13×#104 | C22 | semidirect |
| 41. #88064 | C22 | semidirect |
| 42. #88045 | C22 | semidirect |
| 167. #421 | D13 | semidirect |
| 219. #104 | C2×D13 | semidirect |
| 293. C13 | #3020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88257 | 2 |
| #11719527 | 2 |
| #11719453 | 2 |
| #11719231 | 2 |
| C13×#421 | 2 |
| C2×#88064 | 2 |
| #11718666 | 2 |
| #11718488 | 2 |
| #11718487 | 2 |
| #3020 | 13 |