Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23757577 | C2 | semidirect |
| 4. #23757480 | C2 | semidirect |
| 6. #23757378 | C2 | semidirect |
| 7. C4×#14578944 | C2 | semidirect |
| 95. C157 | #3127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757750 | 2 |
| #23757611 | 2 |
| #23757577 | 2 |
| #23757480 | 2 |
| #23757428 | 2 |
| #23757378 | 2 |
| C4×#14578944 | 2 |
| #23757334 | 2 |
| #541×C157 | 2 |
| #3127 | 157 |