Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
150 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 48. #11929434 | Q16 | semidirect |
| 70. C157 | #1672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757669 | 2 |
| #23757569 | 2 |
| #23757480 | 2 |
| #23757397 | 2 |
| #23757023 | 2 |
| #23757021 | 2 |
| #332×C157 | 2 |
| #1672 | 157 |