Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
216 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 77 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. #23757322 | C2 | semidirect |
| 4. M16×Dic157 | C2 | semidirect |
| 5. #23757045 | C2 | semidirect |
| 6. #23757034 | C2 | semidirect |
| 21. #101×C157 | C4 | semidirect |
| 22. #100×C157 | C4 | semidirect |
| 95. C157 | #1932 | semidirect |
| 115. #101 | Dic157 | semidirect |
| 116. #100 | Dic157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757322 | 2 |
| #23757290 | 2 |
| C2×#19097698 | 2 |
| M16×Dic157 | 2 |
| #23757045 | 2 |
| #23757034 | 2 |
| #413×C157 | 2 |
| #1932 | 157 |