Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
220 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 49 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. #23758078 | C2 | semidirect |
| 2. #23757709 | C2 | semidirect |
| 3. C2×#19097712 | C2 | semidirect |
| 4. #23757085 | C2 | semidirect |
| 5. #23757079 | C2 | semidirect |
| 6. #23757057 | C2 | semidirect |
| 7. #472×C157 | C2 | semidirect |
| 18. #19097711 | C22 | semidirect |
| 19. C2×#14578929 | C22 | semidirect |
| 21. C2×D8×C157 | C22 | semidirect |
| 23. #108×C157 | C22 | semidirect |
| 93. C157 | #2192 | semidirect |
| 98. #472 | D157 | semidirect |
| 110. C2×D8 | C2×D157 | semidirect |
| 117. #108 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23758078 | 2 |
| #23757709 | 2 |
| C2×#19097712 | 2 |
| #23757085 | 2 |
| #23757079 | 2 |
| #23757057 | 2 |
| #472×C157 | 2 |
| #2192 | 157 |