Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #23757309 | C2 | semidirect |
| 3. #23757289 | C2 | semidirect |
| 4. #23757247 | C2 | semidirect |
| 5. #23757246 | C2 | semidirect |
| 6. #23757231 | C2 | semidirect |
| 7. #421×C157 | C2 | semidirect |
| 13. C2×#14578944 | C4 | semidirect |
| 14. C2×#14578942 | C4 | semidirect |
| 15. C2×#14578941 | C4 | semidirect |
| 16. C2×#14578939 | C4 | semidirect |
| 132. C157 | #1976 | semidirect |
| 137. #421 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097791 | 2 |
| #23757309 | 2 |
| #23757289 | 2 |
| #23757247 | 2 |
| #23757246 | 2 |
| #23757231 | 2 |
| #421×C157 | 2 |
| #1976 | 157 |