Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
382 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 73 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. #23757847 | C2 | semidirect |
| 3. C2×#19097760 | C2 | semidirect |
| 4. C2×#19097697 | C2 | semidirect |
| 5. #23757279 | C2 | semidirect |
| 6. #23757034 | C2 | semidirect |
| 7. C2×#101×C157 | C2 | semidirect |
| 130. C157 | #2003 | semidirect |
| 137. C2×#101 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097799 | 2 |
| #23757847 | 2 |
| C2×#19097760 | 2 |
| C2×#19097697 | 2 |
| #23757279 | 2 |
| #23757034 | 2 |
| C2×#101×C157 | 2 |
| #2003 | 157 |