Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
176 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 65 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. #23757352 | C2 | semidirect |
| 3. #23757024 | C2 | semidirect |
| 4. #23757002 | C2 | semidirect |
| 5. #322×C157 | C2 | semidirect |
| 41. C8×C157 | M16 | semidirect |
| 55. C157 | #1594 | semidirect |
| 61. #322 | D157 | semidirect |
| 97. C8 | #14578937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D1256 | 2 |
| #23757352 | 2 |
| #23757024 | 2 |
| #23757002 | 2 |
| #322×C157 | 2 |
| #1594 | 157 |