Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
994 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×D52 | C2 | semidirect |
| 2. C13×#525 | C2 | semidirect |
| 3. C2×#88203 | C2 | semidirect |
| 4. #11718868 | C2 | semidirect |
| 5. #11718707 | C2 | semidirect |
| 6. #11718697 | C2 | semidirect |
| 7. #11718662 | C2 | semidirect |
| 9. C2×C13×#41 | C22 | semidirect |
| 17. C13×C22⋊Q8 | C22 | semidirect |
| 18. C13×#121 | C22 | semidirect |
| 21. C13×#117 | C22 | semidirect |
| 23. C2×#6106 | C22 | semidirect |
| 24. C2×#6104 | C22 | semidirect |
| 25. C2×#6099 | C22 | semidirect |
| 26. C22⋊#1055 | C22 | semidirect |
| 27. #88049 | C22 | semidirect |
| 34. C2×Q8×C13 | C23 | semidirect |
| 37. C2×D4×C13 | C23 | semidirect |
| 50. C2×D52 | D4 | semidirect |
| 53. C13×C4⋊C4 | C23 | semidirect |
| 61. C2×#1055 | C23 | semidirect |
| 96. #525 | D13 | semidirect |
| 108. C22×C13 | AGL(1,ℤ/8) | semidirect |
| 120. C2×#41 | C2×D13 | semidirect |
| 132. C22⋊Q8 | C2×D13 | semidirect |
| 133. #121 | C2×D13 | semidirect |
| 136. #117 | C2×D13 | semidirect |
| 151. C2×Q8 | C22×D13 | semidirect |
| 162. C2×D4 | C22×D13 | semidirect |
| 174. C4⋊C4 | C22×D13 | semidirect |
| 179. C13 | #3003 | semidirect |
| 222. C22 | #88203 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D52 | 2 |
| C13×#525 | 2 |
| C2×#88203 | 2 |
| #11718868 | 2 |
| #11718707 | 2 |
| #11718697 | 2 |
| #11718662 | 2 |
| #3003 | 13 |