Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
456 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 149 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. #23757823 | C2 | semidirect |
| 2. #23757678 | C2 | semidirect |
| 3. #23757650 | C2 | semidirect |
| 4. #23757620 | C2 | semidirect |
| 5. #23757509 | C2 | semidirect |
| 6. C4×D1256 | C2 | semidirect |
| 7. C2×C4×C8×C157 | C2 | semidirect |
| 57. C2×C4×C157 | D8 | semidirect |
| 65. C8×C157 | #41 | semidirect |
| 85. C157 | #3169 | semidirect |
| 93. C2×C4×C8 | D157 | semidirect |
| 143. C2×C4 | D1256 | semidirect |
| 151. C8 | #14578954 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757823 | 2 |
| #23757678 | 2 |
| #23757650 | 2 |
| #23757620 | 2 |
| #23757509 | 2 |
| C4×D1256 | 2 |
| C2×C4×C8×C157 | 2 |
| #3169 | 157 |