Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
272 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 13. #19097700 | C4 | semidirect |
| 15. #19097681 | C4 | semidirect |
| 53. #11929434 | C4⋊C4 | semidirect |
| 84. C157 | #1771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097700 | 2 |
| C2×#19097681 | 2 |
| C2×C4×#11929434 | 2 |
| C4×#14578933 | 2 |
| #23757027 | 2 |
| #336×C157 | 2 |
| #1771 | 157 |