Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
544 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×#19097736 | C2 | semidirect |
| 4. #23757370 | C2 | direct (N × H) |
| 5. C2×#19097704 | C2 | semidirect |
| 6. C2×#19097696 | C2 | semidirect |
| 7. C2×#19097681 | C2 | semidirect |
| 11. C2×#14578942 | C4 | semidirect |
| 15. #19097736 | C22 | semidirect |
| 23. #19097704 | C22 | semidirect |
| 24. #19097696 | C22 | semidirect |
| 25. #19097681 | C22 | semidirect |
| 32. C2×Dic314 | C2×C4 | semidirect |
| 40. #14578942 | C2×C4 | semidirect |
| 41. C2×#11929434 | C2×C4 | semidirect |
| 63. Dic314 | C22×C4 | semidirect |
| 73. #11929434 | C22×C4 | semidirect |
| 106. C2×C157 | #440 | semidirect |
| 110. C157 | C2×#440 | semidirect |
| 217. C2 | #23757370 | 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 |
| C2×#19097736 | 2 |
| C2×D4×Dic157 | 2 |
| #23757370 | 2 |
| C2×#19097704 | 2 |
| C2×#19097696 | 2 |
| C2×#19097681 | 2 |
| C2×#102×C157 | 2 |
| C2×#440 | 157 |