Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. C22×#14578937 | C2 | semidirect |
| 3. C2×#19097692 | C2 | semidirect |
| 4. #23757130 | C2 | semidirect |
| 5. #23757036 | C2 | semidirect |
| 6. #23757035 | C2 | semidirect |
| 7. C2×#102×C157 | C2 | semidirect |
| 15. #19097742 | C4 | semidirect |
| 42. C2×#11929434 | D4 | semidirect |
| 60. C2×C8×C157 | D4 | semidirect |
| 145. C157 | #1895 | semidirect |
| 150. C2×#102 | D157 | semidirect |
| 200. C2×C8 | C22⋊D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578937 | 2 |
| C2×#19097742 | 2 |
| C2×#19097692 | 2 |
| #23757130 | 2 |
| #23757036 | 2 |
| #23757035 | 2 |
| C2×#102×C157 | 2 |
| #1895 | 157 |