Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D317 |
| commutator, socle, cosocle | C22×C317 | C24 |
| Frattini | C22 | C23×D317 |
| Fitting | C4×D4×C317 | C2 |
| hypercenter | C4×D4 | D317 |
| hypocenter | C317 | #525 |
| LCS | G ▷ C22×C317 ▷ C317 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19099574 | C2 | semidirect |
| 2. C22×C4×D317 | C2 | semidirect |
| 3. #23778765 | C2 | semidirect |
| 4. #23778762 | C2 | semidirect |
| 5. #23778758 | C2 | semidirect |
| 6. #23778757 | C2 | semidirect |
| 7. #23778753 | C2 | semidirect |
| 8. #23778752 | C2 | semidirect |
| 9. #23778750 | C2 | semidirect |
| 10. #23778748 | C2 | semidirect |
| 11. C4×D1268 | C2 | semidirect |
| 12. C4×C22⋊D317 | C2 | semidirect |
| 13. C4×C22⋊D317 | C2 | semidirect |
| 14. #23778737 | C2 | semidirect |
| 15. C4×D4×C317 | C2 | semidirect |
| 18. C2×Dic634 | C22 | semidirect |
| 24. C2×C22⋊D317 | C22 | semidirect |
| 31. C2×C4×D317 | C22 | semidirect |
| 32. C4⋊Dic317 | C22 | semidirect |
| 33. #19099553 | C22 | semidirect |
| 34. #19099553 | C22 | semidirect |
| 35. #19099553 | C22 | semidirect |
| 36. #19099553 | C22 | semidirect |
| 38. C22⋊Dic317 | C22 | semidirect |
| 43. #19099551 | C22 | semidirect |
| 44. #19099551 | C22 | semidirect |
| 45. C4×Dic317 | C22 | semidirect |
| 48. C22×C4×C317 | C22 | semidirect |
| 49. C4⋊C4×C317 | C22 | semidirect |
| 51. C22⋊C4×C317 | C22 | semidirect |
| 52. C42×C317 | C22 | semidirect |
| 76. C4×D317 | D4 | semidirect |
| 92. C22×C317 | #41 | semidirect |
| 103. C2×D317 | #41 | semidirect |
| 122. C317 | #525 | semidirect |
| 137. C4×D4 | D317 | semidirect |
| 157. C22×C4 | C2×D317 | semidirect |
| 163. C4⋊C4 | C2×D317 | semidirect |
| 173. C22⋊C4 | C2×D317 | semidirect |
| 175. C42 | C2×D317 | semidirect |
| 225. C22 | #19099574 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099574 | 2 |
| C22×C4×D317 | 2 |
| #23778765 | 2 |
| #23778762 | 2 |
| #23778758 | 2 |
| #23778757 | 2 |
| #23778753 | 2 |
| #23778752 | 2 |
| #23778750 | 2 |
| #23778748 | 2 |
| C4×D1268 | 2 |
| C4×C22⋊D317 | 2 |
| #23778737 | 2 |
| C4×D4×C317 | 2 |
| #525 | 317 |