Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 2. C2×C13×C22⋊Q8 | C2 | semidirect |
| 3. C2×#88196 | C2 | semidirect |
| 4. #11718868 | C2 | semidirect |
| 5. #11718711 | C2 | semidirect |
| 6. #11718708 | C2 | semidirect |
| 7. #11718707 | C2 | semidirect |
| 8. #11718627 | C2 | semidirect |
| 9. C22×Q8×C13 | C22 | semidirect |
| 23. C13×C22⋊Q8 | C22 | semidirect |
| 25. C2×C13×C4⋊C4 | C22 | semidirect |
| 27. C2×#6107 | C22 | semidirect |
| 29. C2×#6106 | C22 | semidirect |
| 30. C2×#6099 | C22 | semidirect |
| 32. C22⋊#1055 | C22 | semidirect |
| 33. #88050 | C22 | semidirect |
| 34. #88049 | C22 | semidirect |
| 120. C2×C22⋊Q8 | D13 | semidirect |
| 135. C22×C13 | #137 | semidirect |
| 154. C22×Q8 | C2×D13 | semidirect |
| 166. C22⋊Q8 | C2×D13 | semidirect |
| 168. C2×C4⋊C4 | C2×D13 | semidirect |
| 224. C13 | #3007 | semidirect |
| 277. C22 | #88196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6127 | 2 |
| C2×C13×C22⋊Q8 | 2 |
| C2×#88196 | 2 |
| #11718868 | 2 |
| #11718711 | 2 |
| #11718708 | 2 |
| #11718707 | 2 |
| #11718627 | 2 |
| #3007 | 13 |