Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23757821 | C2 | semidirect |
| 2. #23757678 | C2 | semidirect |
| 3. #23757619 | C2 | semidirect |
| 4. #23757506 | C2 | semidirect |
| 5. D8×Dic157 | C2 | semidirect |
| 6. C4×C8×D157 | C2 | semidirect |
| 7. #493×C157 | C2 | semidirect |
| 56. C4×D157 | D8 | semidirect |
| 65. C8×C157 | #41 | semidirect |
| 85. C157 | #3169 | semidirect |
| 89. #493 | D157 | semidirect |
| 151. C8 | #14578953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757821 | 2 |
| #23757678 | 2 |
| #23757619 | 2 |
| #23757506 | 2 |
| D8×Dic157 | 2 |
| C4×C8×D157 | 2 |
| #493×C157 | 2 |
| #3169 | 157 |