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. #11719140 | C2 | semidirect |
| 7. C2×#88116 | C2 | semidirect |
| 8. C13×H(5,𝔽2) | C4 | semidirect |
| 10. #88257 | C4 | semidirect |
| 11. #88257 | C4 | semidirect |
| 16. #88251 | 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. #88116 | C22 | semidirect |
| 30. #88116 | C22 | semidirect |
| 31. #88116 | C22 | semidirect |
| 35. C13×#41 | C2×C4 | semidirect |
| 37. C2×D4×C13 | C2×C4 | semidirect |
| 44. Q8×D13 | C2×C4 | semidirect |
| 52. #6129 | C2×C4 | semidirect |
| 57. D4×D13 | C2×C4 | semidirect |
| 62. #6127 | C2×C4 | semidirect |
| 66. C2×Dic26 | C2×C4 | semidirect |
| 146. H(5,𝔽2) | #261 | semidirect |
| 188. #41 | C2×#261 | semidirect |
| 201. C2×D4 | 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 |
|---|---|
| #11719650 | 2 |
| #41×#261 | 2 |
| #11719629 | 2 |
| #11719166 | 2 |
| D13⋊#104 | 2 |
| #11719140 | 2 |
| C2×#88116 | 2 |
| #2901 | 13 |