Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
362 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23757583 | C2 | semidirect |
| 4. #23757579 | C2 | semidirect |
| 5. #23757567 | C2 | semidirect |
| 6. #23757557 | C2 | semidirect |
| 44. C2×Dic314 | Q8 | semidirect |
| 116. C157 | #3082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757904 | 2 |
| #23757750 | 2 |
| #23757583 | 2 |
| #23757579 | 2 |
| #23757567 | 2 |
| #23757557 | 2 |
| #23757309 | 2 |
| #23757301 | 2 |
| #23757283 | 2 |
| C2×#19097694 | 2 |
| #428×C157 | 2 |
| #3082 | 157 |