Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
444 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23757747 | C2 | semidirect |
| 3. #23757278 | C2 | semidirect |
| 4. C2×#19097687 | C2 | semidirect |
| 5. #23757034 | C2 | semidirect |
| 6. #23757032 | C2 | semidirect |
| 7. #418×C157 | C2 | semidirect |
| 12. #19097767 | C4 | semidirect |
| 38. C4⋊Dic157 | D4 | semidirect |
| 43. C4×Dic157 | C2×C4 | semidirect |
| 50. C2×D4×C157 | C2×C4 | semidirect |
| 55. C4⋊C4×C157 | D4 | semidirect |
| 114. C157 | #1887 | semidirect |
| 119. #418 | D157 | semidirect |
| 154. C2×D4 | C4×D157 | semidirect |
| 165. C4⋊C4 | C22⋊D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097767 | 2 |
| #23757747 | 2 |
| #23757278 | 2 |
| C2×#19097687 | 2 |
| #23757034 | 2 |
| #23757032 | 2 |
| #418×C157 | 2 |
| #1887 | 157 |