Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23758001 | C2 | semidirect |
| 3. #23757664 | C2 | semidirect |
| 5. #23757494 | C2 | semidirect |
| 6. #23757484 | C2 | semidirect |
| 7. #23757476 | C2 | semidirect |
| 8. #23757400 | C2 | semidirect |
| 9. #23757370 | C2 | semidirect |
| 10. C4×#14578944 | C2 | semidirect |
| 121. C157 | #3400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758009 | 2 |
| #23758001 | 2 |
| #23757664 | 2 |
| #23757645 | 2 |
| #23757494 | 2 |
| #23757484 | 2 |
| #23757476 | 2 |
| #23757400 | 2 |
| #23757370 | 2 |
| C4×#14578944 | 2 |
| #460×C157 | 2 |
| #3400 | 157 |