Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23758008 | C2 | semidirect |
| 2. #23757944 | C2 | semidirect |
| 3. #23757659 | C2 | semidirect |
| 4. #23757650 | C2 | semidirect |
| 5. #23757491 | C2 | semidirect |
| 6. #23757473 | C2 | semidirect |
| 7. #23757468 | C2 | semidirect |
| 8. #23757467 | C2 | semidirect |
| 9. #23757403 | C2 | semidirect |
| 10. #23757384 | C2 | semidirect |
| 11. C4×SD16×C157 | C2 | semidirect |
| 108. C8×C157 | #41 | semidirect |
| 134. C157 | #3399 | semidirect |
| 146. C4×SD16 | D157 | semidirect |
| 243. C8 | #14578954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758008 | 2 |
| #23757944 | 2 |
| #23757659 | 2 |
| #23757650 | 2 |
| #23757491 | 2 |
| #23757473 | 2 |
| #23757468 | 2 |
| #23757467 | 2 |
| #23757403 | 2 |
| #23757384 | 2 |
| C4×SD16×C157 | 2 |
| #3399 | 157 |