Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
368 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 2. C2×#19097704 | C2 | semidirect |
| 3. C2×#19097692 | C2 | semidirect |
| 4. C2×#19097683 | C2 | semidirect |
| 5. #23757130 | C2 | semidirect |
| 6. #23757036 | C2 | semidirect |
| 7. C2×#102×C157 | C2 | semidirect |
| 40. C2×#11929434 | D4 | semidirect |
| 143. C157 | #2033 | semidirect |
| 148. C2×#102 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097742 | 2 |
| C2×#19097704 | 2 |
| C2×#19097692 | 2 |
| C2×#19097683 | 2 |
| #23757130 | 2 |
| #23757036 | 2 |
| C2×#102×C157 | 2 |
| #2033 | 157 |