Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
726 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 293 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×#19097778 | C2 | semidirect |
| 2. #23757756 | C2 | semidirect |
| 3. #23757282 | C2 | semidirect |
| 4. #23757274 | C2 | semidirect |
| 5. #23757269 | C2 | semidirect |
| 6. C2×#19097695 | C2 | semidirect |
| 21. 2−1+4×C157 | C4 | semidirect |
| 40. #41×C157 | C2×C4 | semidirect |
| 45. C2×Q8×C157 | C2×C4 | semidirect |
| 94. C157 | #2898 | semidirect |
| 104. 2−1+4 | Dic157 | semidirect |
| 125. #41 | C2×Dic157 | semidirect |
| 130. C2×Q8 | C2×Dic157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097778 | 2 |
| #23757756 | 2 |
| #23757282 | 2 |
| #23757274 | 2 |
| #23757269 | 2 |
| C2×#19097695 | 2 |
| C2×2−1+4×C157 | 2 |
| #2898 | 157 |