Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×D628 | C2 | semidirect |
| 3. #23757624 | C2 | semidirect |
| 4. #23757605 | C2 | semidirect |
| 5. #23757558 | C2 | semidirect |
| 6. #23757501 | C2 | semidirect |
| 7. #23757478 | C2 | semidirect |
| 8. #23757410 | C2 | semidirect |
| 9. C8×D628 | C2 | semidirect |
| 10. #103×D157 | C2 | semidirect |
| 11. C4×SD16×C157 | C2 | semidirect |
| 82. D628 | SD16 | semidirect |
| 94. Q8×C157 | #41 | semidirect |
| 128. C157 | #3298 | semidirect |
| 138. C4×SD16 | D157 | semidirect |
| 213. Q8 | #14578954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D628 | 2 |
| #23757928 | 2 |
| #23757624 | 2 |
| #23757605 | 2 |
| #23757558 | 2 |
| #23757501 | 2 |
| #23757478 | 2 |
| #23757410 | 2 |
| C8×D628 | 2 |
| #103×D157 | 2 |
| C4×SD16×C157 | 2 |
| #3298 | 157 |