Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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. #11719527 | C2 | semidirect |
| 2. C2×#88203 | C2 | semidirect |
| 3. C2×#88162 | C2 | semidirect |
| 4. #11719450 | C2 | semidirect |
| 5. C13×#413 | C2 | semidirect |
| 6. C2×#88063 | C2 | semidirect |
| 7. #11718785 | C2 | semidirect |
| 8. #11718415 | C2 | semidirect |
| 9. #11718410 | C2 | semidirect |
| 20. #88196 | C22 | semidirect |
| 21. C2×#6106 | C22 | semidirect |
| 22. #88186 | C22 | semidirect |
| 23. C2×#6104 | C22 | semidirect |
| 28. #88161 | C22 | semidirect |
| 33. C13×#101 | C22 | semidirect |
| 34. C13×#100 | C22 | semidirect |
| 35. #88063 | C22 | semidirect |
| 36. #88062 | C22 | semidirect |
| 130. #413 | D13 | semidirect |
| 174. #101 | C2×D13 | semidirect |
| 176. #100 | C2×D13 | semidirect |
| 230. C13 | #3068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719527 | 2 |
| C2×#88203 | 2 |
| C2×#88162 | 2 |
| #11719450 | 2 |
| C13×#413 | 2 |
| C2×#88063 | 2 |
| #11718785 | 2 |
| #11718415 | 2 |
| #11718410 | 2 |
| #3068 | 13 |