Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
738 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 198 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. #41×#261 | C2 | semidirect |
| 3. #11719629 | C2 | semidirect |
| 4. #11719166 | C2 | semidirect |
| 5. D13⋊#104 | C2 | semidirect |
| 6. #11719155 | C2 | semidirect |
| 7. C2×#88118 | C2 | semidirect |
| 8. C13×2−1+4 | C4 | semidirect |
| 10. #88256 | C4 | semidirect |
| 11. #88256 | C4 | semidirect |
| 16. #88254 | C4 | semidirect |
| 23. #88237 | C22 | semidirect |
| 24. C2×C4×#261 | C22 | semidirect |
| 25. D13⋊M16 | C22 | semidirect |
| 26. C2×#6118 | C22 | semidirect |
| 27. #88118 | C22 | semidirect |
| 28. #88118 | C22 | semidirect |
| 29. #88118 | C22 | semidirect |
| 30. #88116 | C22 | semidirect |
| 31. #88116 | C22 | semidirect |
| 35. C13×#41 | C2×C4 | semidirect |
| 37. C2×Q8×C13 | C2×C4 | semidirect |
| 42. #6131 | C2×C4 | semidirect |
| 46. Q8×D13 | C2×C4 | semidirect |
| 54. D4×D13 | C2×C4 | semidirect |
| 60. #6127 | C2×C4 | semidirect |
| 63. C2×D52 | C2×C4 | semidirect |
| 143. 2−1+4 | #261 | semidirect |
| 188. #41 | C2×#261 | semidirect |
| 193. C2×Q8 | C2×#261 | semidirect |
| 217. C13 | #2901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719652 | 2 |
| #41×#261 | 2 |
| #11719629 | 2 |
| #11719166 | 2 |
| D13⋊#104 | 2 |
| #11719155 | 2 |
| C2×#88118 | 2 |
| #2901 | 13 |