Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D157 | C2 | semidirect |
| 3. #23757566 | C2 | semidirect |
| 4. #23757562 | C2 | semidirect |
| 5. #23757558 | C2 | semidirect |
| 6. #23757554 | C2 | semidirect |
| 7. #23757550 | C2 | semidirect |
| 8. #23757312 | C2 | semidirect |
| 9. #23757295 | C2 | semidirect |
| 11. #475×C157 | C2 | semidirect |
| 44. #14578955 | Q8 | semidirect |
| 88. D628 | C2×Q8 | semidirect |
| 105. Q8×C157 | C2×Q8 | semidirect |
| 137. C157 | #3079 | semidirect |
| 144. #475 | D157 | semidirect |
| 226. Q8 | Q8×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D157 | 2 |
| C4×#14578955 | 2 |
| #23757566 | 2 |
| #23757562 | 2 |
| #23757558 | 2 |
| #23757554 | 2 |
| #23757550 | 2 |
| #23757312 | 2 |
| #23757295 | 2 |
| #23757273 | 2 |
| #475×C157 | 2 |
| #3079 | 157 |