Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. C4×Q8×D157 | C2 | semidirect |
| 3. #23757588 | C2 | semidirect |
| 4. #23757565 | C2 | semidirect |
| 5. #23757474 | C2 | semidirect |
| 6. #23757473 | C2 | semidirect |
| 7. #23757413 | C2 | semidirect |
| 8. #23757376 | C2 | semidirect |
| 9. #23757372 | C2 | semidirect |
| 10. #23757329 | C2 | semidirect |
| 11. #477×C157 | C2 | semidirect |
| 87. Dic314 | #41 | semidirect |
| 108. Q8×C157 | #41 | semidirect |
| 140. C157 | #3112 | semidirect |
| 146. #477 | D157 | semidirect |
| 231. Q8 | #14578955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757824 | 2 |
| C4×Q8×D157 | 2 |
| #23757588 | 2 |
| #23757565 | 2 |
| #23757474 | 2 |
| #23757473 | 2 |
| #23757413 | 2 |
| #23757376 | 2 |
| #23757372 | 2 |
| #23757329 | 2 |
| #477×C157 | 2 |
| #3112 | 157 |