Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
150 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 47 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. #23757653 | C2 | semidirect |
| 4. #23757090 | C2 | semidirect |
| 5. #364×C157 | C2 | semidirect |
| 58. C157 | #2214 | semidirect |
| 63. #364 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757716 | 2 |
| #23757653 | 2 |
| #23757391 | 2 |
| #23757090 | 2 |
| #364×C157 | 2 |
| #2214 | 157 |