Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
362 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19097704 | C2 | semidirect |
| 5. #23757172 | C2 | semidirect |
| 6. #23757027 | C2 | semidirect |
| 7. #340×C157 | C2 | semidirect |
| 19. #19097691 | C4 | semidirect |
| 39. C2×#11929434 | C2×C4 | semidirect |
| 54. C4⋊C4×C157 | C2×C4 | semidirect |
| 66. D628 | C4⋊C4 | semidirect |
| 123. C157 | #1862 | semidirect |
| 130. #340 | D157 | semidirect |
| 175. C4⋊C4 | C4×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097733 | 2 |
| C2×#19097704 | 2 |
| C2×#19097693 | 2 |
| C2×#19097691 | 2 |
| #23757172 | 2 |
| #23757027 | 2 |
| #340×C157 | 2 |
| #1862 | 157 |