Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
572 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 572 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×#19097793 | C2 | semidirect |
| 2. C2×#19097791 | C2 | semidirect |
| 3. #23757819 | C2 | semidirect |
| 4. #23757658 | C2 | semidirect |
| 5. #23757656 | C2 | semidirect |
| 6. #23757654 | C2 | semidirect |
| 7. #23757651 | C2 | semidirect |
| 8. #23757648 | C2 | semidirect |
| 9. #23757644 | C2 | semidirect |
| 10. C2×C8×Dic157 | C2 | semidirect |
| 11. C2×#135×C157 | C2 | semidirect |
| 55. C2×#11929434 | D4 | semidirect |
| 74. C2×C8×C157 | D4 | semidirect |
| 119. Dic157 | #135 | semidirect |
| 125. C157 | #3147 | semidirect |
| 129. C2×#135 | D157 | semidirect |
| 194. C2×C8 | C22⋊D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097793 | 2 |
| C2×#19097791 | 2 |
| #23757819 | 2 |
| #23757658 | 2 |
| #23757656 | 2 |
| #23757654 | 2 |
| #23757651 | 2 |
| #23757648 | 2 |
| #23757644 | 2 |
| C2×C8×Dic157 | 2 |
| C2×#135×C157 | 2 |
| #3147 | 157 |