Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
564 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×#14578942 | C2 | semidirect |
| 2. C23×#11929434 | C2 | semidirect |
| 3. C2×#19097750 | C2 | semidirect |
| 4. #23757500 | C2 | direct (N × H) |
| 5. C2×#19097702 | C2 | semidirect |
| 6. C2×#19097694 | C2 | semidirect |
| 7. C2×#19097692 | C2 | semidirect |
| 11. C2×#14578942 | C22 | semidirect |
| 15. C22×#11929434 | C22 | semidirect |
| 17. #19097750 | C22 | semidirect |
| 21. #19097702 | C22 | semidirect |
| 22. #19097694 | C22 | semidirect |
| 23. #19097692 | C22 | semidirect |
| 40. C2×#11929434 | D4 | semidirect |
| 73. #11929434 | C2×D4 | semidirect |
| 80. C23×C157 | SD16 | semidirect |
| 107. C22×C157 | C2×SD16 | semidirect |
| 119. C2×C157 | #465 | semidirect |
| 123. C157 | C2×#465 | semidirect |
| 195. C23 | #14578942 | semidirect |
| 231. C22 | C2×#14578942 | semidirect |
| 243. C2 | #23757500 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578942 | 2 |
| C23×#11929434 | 2 |
| C2×#19097750 | 2 |
| #23757500 | 2 |
| C2×#19097702 | 2 |
| C2×#19097694 | 2 |
| C2×#19097692 | 2 |
| C2×#121×C157 | 2 |
| C2×#465 | 157 |