Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#14578943 | C2 | semidirect |
| 4. #23757750 | C2 | semidirect |
| 5. #23757496 | C2 | semidirect |
| 6. #23757474 | C2 | semidirect |
| 7. #23757279 | C2 | semidirect |
| 8. #23757270 | C2 | semidirect |
| 9. #424×C157 | C2 | semidirect |
| 14. C2×Dic628 | C22 | semidirect |
| 17. C2×#14578943 | C22 | semidirect |
| 22. C4×Dic314 | C22 | semidirect |
| 26. #19097696 | C22 | semidirect |
| 28. #19097693 | C22 | semidirect |
| 32. C4⋊C8×C157 | C22 | semidirect |
| 38. C2×Dic314 | D4 | semidirect |
| 116. C157 | #3043 | semidirect |
| 124. #424 | D157 | semidirect |
| 146. C4⋊C8 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097804 | 2 |
| C22×#14578943 | 2 |
| #23757842 | 2 |
| #23757750 | 2 |
| #23757496 | 2 |
| #23757474 | 2 |
| #23757279 | 2 |
| #23757270 | 2 |
| #424×C157 | 2 |
| #3043 | 157 |