Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#88162 | C2 | semidirect |
| 2. C2×#88128 | C2 | semidirect |
| 3. C4×#6127 | C2 | semidirect |
| 4. C13×#423 | C2 | semidirect |
| 5. #11718792 | C2 | semidirect |
| 6. #11718509 | C2 | semidirect |
| 7. #11718504 | C2 | semidirect |
| 16. C2×D104 | C22 | semidirect |
| 17. C2×#6095 | C22 | semidirect |
| 21. C4×D52 | C22 | semidirect |
| 24. C4×Dic26 | C22 | semidirect |
| 25. C13×C4⋊C8 | C22 | semidirect |
| 26. #88061 | C22 | semidirect |
| 32. #6127 | D4 | semidirect |
| 79. D52 | C2×D4 | semidirect |
| 83. Dic26 | C2×D4 | semidirect |
| 90. #423 | D13 | semidirect |
| 102. C4×C13 | AGL(1,ℤ/8) | semidirect |
| 124. C4⋊C8 | C2×D13 | semidirect |
| 161. C13 | #3038 | semidirect |
| 201. C4 | #88162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88162 | 2 |
| C2×#88128 | 2 |
| C4×#6127 | 2 |
| C13×#423 | 2 |
| #11718792 | 2 |
| #11718509 | 2 |
| #11718504 | 2 |
| #3038 | 13 |