Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
406 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 1. #23757945 | C2 | semidirect |
| 2. #23757663 | C2 | semidirect |
| 3. #23757647 | C2 | semidirect |
| 4. #23757485 | C2 | semidirect |
| 5. #23757475 | C2 | semidirect |
| 6. #23757473 | C2 | semidirect |
| 7. #23757468 | C2 | semidirect |
| 8. #23757404 | C2 | semidirect |
| 9. #23757371 | C2 | semidirect |
| 10. C4×#14578939 | C2 | semidirect |
| 11. #556×C157 | C2 | semidirect |
| 92. #11929434 | #41 | semidirect |
| 132. C157 | #3397 | semidirect |
| 134. #556 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757945 | 2 |
| #23757663 | 2 |
| #23757647 | 2 |
| #23757485 | 2 |
| #23757475 | 2 |
| #23757473 | 2 |
| #23757468 | 2 |
| #23757404 | 2 |
| #23757371 | 2 |
| C4×#14578939 | 2 |
| #556×C157 | 2 |
| #3397 | 157 |