Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
540 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 540 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. #23757177 | C2 | semidirect |
| 3. #23757164 | C2 | semidirect |
| 4. #23757163 | C2 | semidirect |
| 6. #23757144 | C2 | semidirect |
| 7. #23757141 | C2 | semidirect |
| 8. C4×#14578931 | C2 | semidirect |
| 9. C4×C4⋊C4×C157 | C2 | semidirect |
| 13. #19097759 | C4 | semidirect |
| 34. C2×Dic314 | C2×C4 | semidirect |
| 47. #14578931 | C2×C4 | semidirect |
| 48. #14578931 | C2×C4 | semidirect |
| 58. C42×C157 | C2×C4 | semidirect |
| 118. C157 | #2337 | semidirect |
| 127. C4×C4⋊C4 | D157 | semidirect |
| 177. C42 | C4×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097759 | 2 |
| #23757177 | 2 |
| #23757164 | 2 |
| #23757163 | 2 |
| #23757151 | 2 |
| #23757144 | 2 |
| #23757141 | 2 |
| C4×#14578931 | 2 |
| C4×C4⋊C4×C157 | 2 |
| #2337 | 157 |