Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#19097794 | C2 | semidirect |
| 2. C2×Q16×D157 | C2 | semidirect |
| 3. #23757935 | C2 | semidirect |
| 4. #23757657 | C2 | semidirect |
| 5. #23757515 | C2 | semidirect |
| 6. #23757510 | C2 | semidirect |
| 7. #23757495 | C2 | semidirect |
| 8. #23757438 | C2 | semidirect |
| 9. #23757413 | C2 | semidirect |
| 10. C8×D628 | C2 | semidirect |
| 11. C4×Q16×C157 | C2 | semidirect |
| 73. Q16×C157 | D4 | semidirect |
| 120. C2×D157 | #135 | semidirect |
| 136. C157 | #3285 | semidirect |
| 147. C4×Q16 | D157 | semidirect |
| 195. Q16 | D628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097794 | 2 |
| C2×Q16×D157 | 2 |
| #23757935 | 2 |
| #23757657 | 2 |
| #23757515 | 2 |
| #23757510 | 2 |
| #23757495 | 2 |
| #23757438 | 2 |
| #23757413 | 2 |
| C8×D628 | 2 |
| C4×Q16×C157 | 2 |
| #3285 | 157 |