Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
164 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 55 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. C2×#19097714 | C2 | semidirect |
| 2. C22×#14578929 | C2 | semidirect |
| 4. #23757100 | C2 | semidirect |
| 5. #23757077 | C2 | semidirect |
| 6. #23757073 | C2 | semidirect |
| 7. #467×C157 | C2 | semidirect |
| 28. #14578929 | D4 | semidirect |
| 59. C22×C157 | SD32 | semidirect |
| 75. C157 | #2217 | semidirect |
| 79. #467 | D157 | semidirect |
| 138. C22 | #19097714 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097714 | 2 |
| C22×#14578929 | 2 |
| #23757509 | 2 |
| #23757100 | 2 |
| #23757077 | 2 |
| #23757073 | 2 |
| #467×C157 | 2 |
| #2217 | 157 |