Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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. #23757830 | C2 | semidirect |
| 3. #23757671 | C2 | semidirect |
| 4. #23757646 | C2 | semidirect |
| 5. #23757624 | C2 | semidirect |
| 6. #23757620 | C2 | semidirect |
| 7. #23757502 | C2 | semidirect |
| 8. C4×#14578943 | C2 | semidirect |
| 9. C2×C4×C8×C157 | C2 | semidirect |
| 82. C2×C4×C157 | SD16 | semidirect |
| 90. C8×C157 | #41 | semidirect |
| 112. C157 | #3167 | semidirect |
| 122. C2×C4×C8 | D157 | semidirect |
| 195. C2×C4 | #14578943 | semidirect |
| 203. C8 | #14578954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757830 | 2 |
| #23757823 | 2 |
| #23757671 | 2 |
| #23757646 | 2 |
| #23757624 | 2 |
| #23757620 | 2 |
| #23757502 | 2 |
| C4×#14578943 | 2 |
| C2×C4×C8×C157 | 2 |
| #3167 | 157 |