Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
304 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. #23757281 | C2 | semidirect |
| 4. C2×#19097689 | C2 | semidirect |
| 5. #23757043 | C2 | semidirect |
| 6. #23757031 | C2 | semidirect |
| 11. C2×#14578944 | C4 | semidirect |
| 12. C2×#14578942 | C4 | semidirect |
| 107. C157 | #1902 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097801 | 2 |
| #23758040 | 2 |
| #23757281 | 2 |
| C2×#19097689 | 2 |
| #23757043 | 2 |
| #23757031 | 2 |
| #421×C157 | 2 |
| #1902 | 157 |