Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 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. #11719510 | C2 | semidirect |
| 2. C22×#6104 | C2 | semidirect |
| 3. C2×#88162 | C2 | semidirect |
| 4. #11719226 | C2 | semidirect |
| 5. C13×#418 | C2 | semidirect |
| 6. #11718780 | C2 | semidirect |
| 7. #11718663 | C2 | semidirect |
| 8. #11718448 | C2 | semidirect |
| 9. #11718447 | C2 | semidirect |
| 16. #88194 | C22 | semidirect |
| 18. #88190 | C22 | semidirect |
| 24. C2×D104 | C22 | semidirect |
| 25. C2×#6095 | C22 | semidirect |
| 26. #88147 | C22 | semidirect |
| 29. C13×#102 | C22 | semidirect |
| 30. #88054 | C22 | semidirect |
| 31. #88050 | C22 | semidirect |
| 32. #88049 | C22 | semidirect |
| 46. C2×D52 | D4 | semidirect |
| 106. #418 | D13 | semidirect |
| 147. #102 | C2×D13 | semidirect |
| 188. C13 | #3041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719510 | 2 |
| C22×#6104 | 2 |
| C2×#88162 | 2 |
| #11719226 | 2 |
| C13×#418 | 2 |
| #11718780 | 2 |
| #11718663 | 2 |
| #11718448 | 2 |
| #11718447 | 2 |
| #3041 | 13 |