Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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. #23757591 | C2 | direct (N × H) |
| 3. C2×#19097702 | C2 | semidirect |
| 4. C2×#19097691 | C2 | semidirect |
| 5. C2×C22⋊#11929434 | C2 | semidirect |
| 6. C22×C4⋊C4×C157 | C2 | semidirect |
| 14. #19097702 | C22 | semidirect |
| 15. #19097691 | C22 | semidirect |
| 16. C22⋊#11929434 | C22 | semidirect |
| 22. C2×C4⋊C4×C157 | C22 | semidirect |
| 90. C2×C157 | #481 | semidirect |
| 95. C157 | C2×#481 | semidirect |
| 98. C22×C4⋊C4 | D157 | semidirect |
| 114. C2×C4⋊C4 | C2×D157 | semidirect |
| 187. C2 | #23757591 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097745 | 2 |
| #23757591 | 2 |
| C2×#19097702 | 2 |
| C2×#19097691 | 2 |
| C2×C22⋊#11929434 | 2 |
| C22×C4⋊C4×C157 | 2 |
| C2×#481 | 157 |