Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
484 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 153 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×#19097802 | C2 | semidirect |
| 3. #23757495 | C2 | semidirect |
| 4. #23757483 | C2 | semidirect |
| 5. #23757473 | C2 | semidirect |
| 6. #23757297 | C2 | semidirect |
| 7. #23757272 | C2 | semidirect |
| 8. C2×C4×Q8×C157 | C2 | semidirect |
| 52. C2×Q8×C157 | D4 | semidirect |
| 111. C4×C157 | #137 | semidirect |
| 120. C157 | #3037 | semidirect |
| 124. C2×C4×Q8 | D157 | semidirect |
| 160. C2×Q8 | D628 | semidirect |
| 233. C4 | #19097802 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097802 | 2 |
| #23757823 | 2 |
| #23757495 | 2 |
| #23757483 | 2 |
| #23757473 | 2 |
| #23757297 | 2 |
| #23757272 | 2 |
| C2×C4×Q8×C157 | 2 |
| #3037 | 157 |