Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
5956 conjugacy classes of subgroups; only the 3205 normal subgroups are shown.
This group has 5956 conjugacy classes of subgroups — too many to draw. Only its 3205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C24×D13 |
| commutator, cosocle | C2×C13 | C26 |
| Frattini | C2 | C25×D13 |
| Fitting | C2×C13×H(5,𝔽2) | C2 |
| socle | C22×C13 | C25 |
| hypercenter | C2×H(5,𝔽2) | D13 |
| hypocenter | C13 | C2×#585 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C2×H(5,𝔽2) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C13×H(5,𝔽2) | C2 | semidirect |
| 2. #11719650 | C2 | direct (N × H) |
| 3. C2×#88257 | C2 | semidirect |
| 4. C2×#41×D13 | C2 | semidirect |
| 5. C2×#88251 | C2 | semidirect |
| 6. C22×#6129 | C2 | semidirect |
| 7. C13×H(5,𝔽2) | C22 | semidirect |
| 8. C2×C13×#41 | C22 | semidirect |
| 9. C22×D4×C13 | C22 | semidirect |
| 10. C22×C22⋊D13 | C22 | semidirect |
| 11. C23×Dic13 | C22 | semidirect |
| 12. #88257 | C22 | semidirect |
| 13. #41×D13 | C22 | semidirect |
| 14. C2×#6131 | C22 | semidirect |
| 15. C2×Q8×D13 | C22 | semidirect |
| 16. #88251 | C22 | semidirect |
| 17. C2×#6129 | C22 | semidirect |
| 18. C2×#6129 | C22 | semidirect |
| 19. C2×#6129 | C22 | semidirect |
| 20. C2×D4×D13 | C22 | semidirect |
| 21. C2×#6127 | C22 | semidirect |
| 22. C22×C4×D13 | C22 | semidirect |
| 23. C22×Dic26 | C22 | semidirect |
| 26. C13×#41 | C23 | semidirect |
| 29. C2×D4×C13 | C23 | semidirect |
| 32. C2×C22⋊D13 | C23 | semidirect |
| 35. C22×Dic13 | C23 | semidirect |
| 36. #6131 | C23 | semidirect |
| 37. Q8×D13 | C23 | semidirect |
| 38. #6129 | C23 | semidirect |
| 39. #6129 | C23 | semidirect |
| 40. D4×D13 | C23 | semidirect |
| 41. #6127 | C23 | semidirect |
| 45. C2×C4×D13 | C23 | semidirect |
| 47. C2×Dic26 | C23 | semidirect |
| 71. C2×H(5,𝔽2) | D13 | semidirect |
| 86. H(5,𝔽2) | C2×D13 | semidirect |
| 93. C2×#41 | C2×D13 | semidirect |
| 98. C22×D4 | C2×D13 | semidirect |
| 102. C2×C13 | #585 | semidirect |
| 111. #41 | C22×D13 | semidirect |
| 121. C2×D4 | C22×D13 | semidirect |
| 129. C13 | C2×#585 | semidirect |
| 161. C2 | #11719650 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×H(5,𝔽2) | 2 |
| #11719650 | 2 |
| C2×#88257 | 2 |
| C2×#41×D13 | 2 |
| C2×#88251 | 2 |
| C22×#6129 | 2 |
| C2×#585 | 13 |