Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19097771 | C2 | semidirect |
| 3. #23757569 | C2 | semidirect |
| 4. #23757564 | C2 | semidirect |
| 5. #23757559 | C2 | semidirect |
| 6. #23757554 | C2 | semidirect |
| 7. #23757315 | C2 | semidirect |
| 9. #423×C157 | C2 | semidirect |
| 36. #14578954 | Q8 | semidirect |
| 74. Dic314 | C2×Q8 | semidirect |
| 76. D628 | C2×Q8 | semidirect |
| 121. C157 | #3079 | semidirect |
| 130. #423 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097771 | 2 |
| C4×#14578954 | 2 |
| #23757569 | 2 |
| #23757564 | 2 |
| #23757559 | 2 |
| #23757554 | 2 |
| #23757315 | 2 |
| #23757275 | 2 |
| #423×C157 | 2 |
| #3079 | 157 |