Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
198 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 53 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. C2×#19097716 | C2 | semidirect |
| 2. C2×#19097715 | C2 | semidirect |
| 3. C2×#19097712 | C2 | semidirect |
| 4. #23757656 | C2 | semidirect |
| 5. #23757648 | C2 | semidirect |
| 6. #23757048 | C2 | semidirect |
| 7. C2×D16×C157 | C2 | semidirect |
| 35. #14578929 | D4 | semidirect |
| 43. C16×C157 | D4 | semidirect |
| 78. C157 | #2250 | semidirect |
| 83. C2×D16 | D157 | semidirect |
| 122. C16 | C22⋊D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097716 | 2 |
| C2×#19097715 | 2 |
| C2×#19097712 | 2 |
| #23757656 | 2 |
| #23757648 | 2 |
| #23757048 | 2 |
| C2×D16×C157 | 2 |
| #2250 | 157 |