Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 1. #23758288 | C2 | semidirect |
| 4. M16×#10597845 | C2 | semidirect |
| 5. #23758156 | C2 | semidirect |
| 6. #23758145 | C2 | semidirect |
| 23. #19097690 | C4 | semidirect |
| 24. #19097687 | C4 | semidirect |
| 25. #19097687 | C4 | semidirect |
| 26. #101×C157 | C4 | semidirect |
| 105. C157 | #1932 | semidirect |
| 128. #101 | #10597845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758288 | 2 |
| #23758272 | 2 |
| C2×#19097836 | 2 |
| M16×#10597845 | 2 |
| #23758156 | 2 |
| #23758145 | 2 |
| #23757256 | 2 |
| #1932 | 157 |