Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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. #11719535 | C2 | semidirect |
| 2. C2×#88204 | C2 | semidirect |
| 3. C2×#88162 | C2 | semidirect |
| 4. #11719209 | C2 | semidirect |
| 5. C13×#417 | C2 | semidirect |
| 6. #11718780 | C2 | semidirect |
| 7. C2×#88049 | C2 | semidirect |
| 8. #11718480 | C2 | semidirect |
| 9. #11718459 | C2 | semidirect |
| 10. #11718447 | C2 | semidirect |
| 11. #11718423 | C2 | semidirect |
| 19. C2×#6107 | C22 | semidirect |
| 20. C2×#6106 | C22 | semidirect |
| 23. C2×#6105 | C22 | semidirect |
| 24. C2×#6104 | C22 | semidirect |
| 33. #88147 | C22 | semidirect |
| 36. #88141 | C22 | semidirect |
| 37. C13×#103 | C22 | semidirect |
| 38. C13×#102 | C22 | semidirect |
| 39. #88054 | C22 | semidirect |
| 40. #88054 | C22 | semidirect |
| 56. #6127 | D4 | semidirect |
| 135. #417 | D13 | semidirect |
| 186. #103 | C2×D13 | semidirect |
| 189. #102 | C2×D13 | semidirect |
| 241. C13 | #3045 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719535 | 2 |
| C2×#88204 | 2 |
| C2×#88162 | 2 |
| #11719209 | 2 |
| C13×#417 | 2 |
| #11718780 | 2 |
| C2×#88049 | 2 |
| #11718480 | 2 |
| #11718459 | 2 |
| #11718447 | 2 |
| #11718423 | 2 |
| #3045 | 13 |