Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
342 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 119 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. C22×C4×D317 | C2 | semidirect |
| 3. #23778765 | C2 | direct (N × H) |
| 4. C2×#19099553 | C2 | semidirect |
| 5. C2×#19099551 | C2 | semidirect |
| 6. C2×#19099551 | C2 | semidirect |
| 7. C2×#19099551 | C2 | semidirect |
| 8. C2×C4⋊C4×C317 | C2 | semidirect |
| 16. C2×C4×D317 | C22 | semidirect |
| 17. #19099553 | C22 | semidirect |
| 18. #19099551 | C22 | semidirect |
| 19. #19099551 | C22 | semidirect |
| 20. #19099551 | C22 | semidirect |
| 24. C4⋊C4×C317 | C22 | semidirect |
| 63. C2×C317 | #123 | semidirect |
| 69. C317 | C2×#123 | semidirect |
| 75. C2×C4⋊C4 | D317 | semidirect |
| 91. C4⋊C4 | C2×D317 | semidirect |
| 135. C2 | #23778765 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1268 | 2 |
| C22×C4×D317 | 2 |
| #23778765 | 2 |
| C2×#19099553 | 2 |
| C2×#19099551 | 2 |
| C2×C4⋊C4×C317 | 2 |
| C2×#123 | 317 |