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. #11719538 | C2 | semidirect |
| 2. C2×#88203 | C2 | semidirect |
| 3. C2×#88155 | C2 | semidirect |
| 4. #11719230 | C2 | semidirect |
| 5. C13×#416 | C2 | semidirect |
| 6. C2×#88061 | C2 | semidirect |
| 7. #11718656 | C2 | semidirect |
| 8. #11718473 | C2 | semidirect |
| 9. #11718468 | C2 | semidirect |
| 10. #11718443 | C2 | semidirect |
| 11. #11718436 | C2 | semidirect |
| 18. #88200 | C22 | semidirect |
| 21. #88192 | C22 | semidirect |
| 28. C2×#6094 | C22 | semidirect |
| 29. C2×C8×D13 | C22 | semidirect |
| 35. C13×#103 | C22 | semidirect |
| 36. C13×#103 | C22 | semidirect |
| 37. C13×#102 | C22 | semidirect |
| 38. C13×#102 | C22 | semidirect |
| 41. #88048 | C22 | semidirect |
| 42. #88047 | C22 | semidirect |
| 81. #6099 | D4 | semidirect |
| 132. #416 | D13 | semidirect |
| 181. #103 | C2×D13 | semidirect |
| 182. #103 | C2×D13 | semidirect |
| 185. #102 | C2×D13 | semidirect |
| 186. #102 | C2×D13 | semidirect |
| 236. C13 | #3062 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719538 | 2 |
| C2×#88203 | 2 |
| C2×#88155 | 2 |
| #11719230 | 2 |
| C13×#416 | 2 |
| C2×#88061 | 2 |
| #11718656 | 2 |
| #11718473 | 2 |
| #11718468 | 2 |
| #11718443 | 2 |
| #11718436 | 2 |
| #3062 | 13 |