Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
528 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 157 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×#19097770 | C2 | semidirect |
| 3. #23757618 | C2 | direct (N × H) |
| 4. C2×#19097693 | C2 | semidirect |
| 5. C2×#19097692 | C2 | semidirect |
| 6. C2×#19097691 | C2 | semidirect |
| 7. C2×C8×Dic157 | C2 | semidirect |
| 8. C2×#102×C157 | C2 | semidirect |
| 15. #19097770 | C22 | semidirect |
| 21. #19097693 | C22 | semidirect |
| 22. #19097692 | C22 | semidirect |
| 23. #19097691 | C22 | semidirect |
| 24. C8×Dic157 | C22 | semidirect |
| 28. #102×C157 | C22 | semidirect |
| 113. C2×C157 | #486 | semidirect |
| 118. C157 | C2×#486 | semidirect |
| 126. C2×#102 | D157 | semidirect |
| 146. #102 | C2×D157 | semidirect |
| 233. C2 | #23757618 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097770 | 2 |
| C2×#19097767 | 2 |
| #23757618 | 2 |
| C2×#19097693 | 2 |
| C2×#19097692 | 2 |
| C2×#19097691 | 2 |
| C2×C8×Dic157 | 2 |
| C2×#102×C157 | 2 |
| C2×#486 | 157 |