Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
380 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 157 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. #23757679 | C2 | semidirect |
| 3. #23757676 | C2 | semidirect |
| 4. #23757669 | C2 | semidirect |
| 31. #14578938 | Q8 | semidirect |
| 60. #11929434 | C2×Q8 | semidirect |
| 92. C157 | #3165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757830 | 2 |
| #23757679 | 2 |
| #23757676 | 2 |
| #23757669 | 2 |
| #23757313 | 2 |
| C4×#14578938 | 2 |
| C2×C4⋊Q8×C157 | 2 |
| #3165 | 157 |