Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
362 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #23757582 | C2 | semidirect |
| 4. #23757578 | C2 | semidirect |
| 5. #23757566 | C2 | semidirect |
| 6. #23757556 | C2 | semidirect |
| 65. C2×Q8×C157 | Q8 | semidirect |
| 116. C157 | #3082 | semidirect |
| 161. C2×Q8 | Dic314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757901 | 2 |
| #23757751 | 2 |
| #23757582 | 2 |
| #23757578 | 2 |
| #23757566 | 2 |
| #23757556 | 2 |
| #23757315 | 2 |
| #23757309 | 2 |
| #23757301 | 2 |
| C2×#19097695 | 2 |
| #419×C157 | 2 |
| #3082 | 157 |