Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
396 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 3. C2×C8×#10597845 | C2 | semidirect |
| 4. C4⋊C4×#10597845 | C2 | semidirect |
| 5. #23758147 | C2 | semidirect |
| 6. #23758146 | C2 | semidirect |
| 11. D4×#10597845 | C4 | semidirect |
| 17. #19097833 | C4 | semidirect |
| 23. #19097693 | C4 | semidirect |
| 24. #19097692 | C4 | semidirect |
| 25. #19097691 | C4 | semidirect |
| 26. #102×C157 | C4 | semidirect |
| 35. D157⋊C8 | C2×C4 | semidirect |
| 40. C4⋊#10597845 | C2×C4 | semidirect |
| 54. C2×#11929434 | C2×C4 | semidirect |
| 57. C4⋊Dic157 | C2×C4 | semidirect |
| 60. C2×C8×C157 | C2×C4 | semidirect |
| 61. C4⋊C4×C157 | C2×C4 | semidirect |
| 85. D628 | C42 | semidirect |
| 99. D4×C157 | C42 | semidirect |
| 123. #10597845 | #102 | direct (N × H) |
| 139. C157 | C4×#102 | semidirect |
| 164. #102 | #10597845 | direct (N × H) |
| 190. C2×C8 | C2×#10597845 | semidirect |
| 197. C4⋊C4 | C2×#10597845 | semidirect |
| 216. D4 | C4×#10597845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#10597845 | 2 |
| C2×#19097833 | 2 |
| C2×C8×#10597845 | 2 |
| C4⋊C4×#10597845 | 2 |
| #23758147 | 2 |
| #23758146 | 2 |
| #102×D157 | 2 |
| C4×#102 | 157 |