Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11719182 | C2 | semidirect |
| 2. C2×#88129 | C2 | semidirect |
| 3. C13×#432 | C2 | semidirect |
| 4. #11718505 | C2 | semidirect |
| 5. #11718399 | C2 | semidirect |
| 6. #11718393 | C2 | semidirect |
| 7. #11718375 | C2 | semidirect |
| 8. #11718373 | C2 | semidirect |
| 18. C2×#6095 | C22 | semidirect |
| 24. #88128 | C22 | semidirect |
| 26. C4×D52 | C22 | semidirect |
| 27. #88123 | C22 | semidirect |
| 28. C13×C4⋊C8 | C22 | semidirect |
| 30. C13×#97 | C22 | semidirect |
| 32. #88056 | C22 | semidirect |
| 103. #432 | D13 | semidirect |
| 142. C4⋊C8 | C2×D13 | semidirect |
| 146. #97 | C2×D13 | semidirect |
| 186. C13 | #3213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719182 | 2 |
| C2×#88129 | 2 |
| C13×#432 | 2 |
| #11718505 | 2 |
| #11718399 | 2 |
| #11718393 | 2 |
| #11718375 | 2 |
| #11718373 | 2 |
| #3213 | 13 |