Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
958 conjugacy classes of subgroups; only the 449 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 449 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D13 |
| commutator, socle, cosocle | C22×C13 | C25 |
| Fitting | C13×H(3,𝔽4) | C2 |
| hypercenter | H(3,𝔽4) | D13 |
| hypocenter | C13 | #3568 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×H(3,𝔽4) | C2 | semidirect |
| 2. #11719385 | C2 | semidirect |
| 3. #11719377 | C2 | semidirect |
| 4. #11719376 | C2 | semidirect |
| 5. #11719374 | C2 | semidirect |
| 6. #11719298 | C2 | semidirect |
| 7. #11719292 | C2 | semidirect |
| 11. #88207 | C22 | semidirect |
| 12. C2×C22⋊Dic13 | C22 | semidirect |
| 13. #88200 | C22 | semidirect |
| 14. Q8×Dic13 | C22 | semidirect |
| 15. #88198 | C22 | semidirect |
| 23. #88139 | C22 | semidirect |
| 24. #88137 | C22 | semidirect |
| 25. #88135 | C22 | semidirect |
| 26. #88133 | C22 | semidirect |
| 27. #88133 | C22 | semidirect |
| 28. #88133 | C22 | semidirect |
| 29. #88133 | C22 | semidirect |
| 30. #88132 | C22 | semidirect |
| 31. #88132 | C22 | semidirect |
| 32. #88132 | C22 | semidirect |
| 33. #88131 | C22 | semidirect |
| 34. #88131 | C22 | semidirect |
| 35. #88130 | C22 | semidirect |
| 36. C42×D13 | C22 | semidirect |
| 37. #88124 | C22 | semidirect |
| 38. C4×Dic26 | C22 | semidirect |
| 88. H(3,𝔽4) | D13 | semidirect |
| 170. C13 | #3568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×H(3,𝔽4) | 2 |
| #11719385 | 2 |
| #11719377 | 2 |
| #11719376 | 2 |
| #11719374 | 2 |
| #11719298 | 2 |
| #11719292 | 2 |
| #3568 | 13 |