Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
552 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#19097804 | C2 | semidirect |
| 2. C2×#19097802 | C2 | semidirect |
| 3. C2×#19097801 | C2 | semidirect |
| 5. C2×#19097769 | C2 | semidirect |
| 6. #23757666 | C2 | semidirect |
| 7. #23757664 | C2 | semidirect |
| 8. #23757651 | C2 | semidirect |
| 9. #23757644 | C2 | semidirect |
| 10. M16×Dic157 | C2 | semidirect |
| 11. C2×#137×C157 | C2 | semidirect |
| 62. #14578938 | D4 | semidirect |
| 86. M16×C157 | D4 | semidirect |
| 140. Dic157 | #137 | semidirect |
| 146. C157 | #3152 | semidirect |
| 151. C2×#137 | D157 | semidirect |
| 224. M16 | C22⋊D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097804 | 2 |
| C2×#19097802 | 2 |
| C2×#19097801 | 2 |
| #23757819 | 2 |
| C2×#19097769 | 2 |
| #23757666 | 2 |
| #23757664 | 2 |
| #23757651 | 2 |
| #23757644 | 2 |
| M16×Dic157 | 2 |
| C2×#137×C157 | 2 |
| #3152 | 157 |