Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #23757750 | C2 | semidirect |
| 4. #23757370 | C2 | semidirect |
| 5. #23757364 | C2 | semidirect |
| 6. #23757309 | C2 | semidirect |
| 7. #23757283 | C2 | semidirect |
| 8. #23757231 | C2 | semidirect |
| 11. C2×#14578942 | C4 | semidirect |
| 16. #19097736 | C22 | semidirect |
| 23. #19097704 | C22 | semidirect |
| 24. #19097702 | C22 | semidirect |
| 25. #19097696 | C22 | semidirect |
| 26. #19097681 | C22 | semidirect |
| 27. C8×Dic157 | C22 | semidirect |
| 34. C2×Dic314 | C2×C4 | semidirect |
| 38. #14578942 | C2×C4 | semidirect |
| 39. #14578942 | C2×C4 | semidirect |
| 40. C2×#11929434 | C2×C4 | semidirect |
| 103. C157 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578942 | 2 |
| #23757750 | 2 |
| #23757748 | 2 |
| #23757370 | 2 |
| #23757364 | 2 |
| #23757309 | 2 |
| #23757283 | 2 |
| #23757231 | 2 |
| #418×C157 | 2 |
| #2949 | 157 |