Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
320 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 88 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. M16×#10597845 | C2 | semidirect |
| 4. #23758209 | C2 | semidirect |
| 5. #23758145 | C2 | semidirect |
| 6. #23758144 | C2 | semidirect |
| 9. Q8×#10597845 | C4 | semidirect |
| 11. D4×#10597845 | C4 | semidirect |
| 17. #19097836 | C4 | semidirect |
| 18. #19097835 | C4 | semidirect |
| 25. #19097699 | C4 | semidirect |
| 26. #19097698 | C4 | semidirect |
| 27. #19097697 | C4 | semidirect |
| 28. #104×C157 | C4 | semidirect |
| 32. #14578964 | C2×C4 | semidirect |
| 43. C4×#10597845 | C2×C4 | semidirect |
| 57. #14578938 | C2×C4 | semidirect |
| 61. C4×Dic157 | C2×C4 | semidirect |
| 63. M16×C157 | C2×C4 | semidirect |
| 64. C42×C157 | C2×C4 | semidirect |
| 126. C157 | #1759 | semidirect |
| 152. #104 | #10597845 | semidirect |
| 175. M16 | C2×#10597845 | semidirect |
| 191. C42 | C2×#10597845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#10597845 | 2 |
| D157⋊#104 | 2 |
| M16×#10597845 | 2 |
| #23758209 | 2 |
| #23758145 | 2 |
| #23758144 | 2 |
| #104×D157 | 2 |
| #1759 | 157 |