Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
496 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 91 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×#14578939 | C2 | semidirect |
| 2. C2×#19097746 | C2 | semidirect |
| 3. C2×#19097742 | C2 | semidirect |
| 4. C2×#19097693 | C2 | semidirect |
| 5. C2×#19097683 | C2 | semidirect |
| 6. #23757035 | C2 | semidirect |
| 7. C2×#102×C157 | C2 | semidirect |
| 39. C2×D628 | D4 | semidirect |
| 54. C2×#11929434 | D4 | semidirect |
| 56. C4⋊Dic157 | D4 | semidirect |
| 65. C2×D4×C157 | D4 | semidirect |
| 72. C4⋊C4×C157 | D4 | semidirect |
| 86. C22×D157 | D8 | semidirect |
| 171. C157 | #1999 | semidirect |
| 177. C2×#102 | D157 | semidirect |
| 221. C2×D4 | D628 | semidirect |
| 242. C4⋊C4 | C22⋊D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14578939 | 2 |
| C2×#19097746 | 2 |
| C2×#19097742 | 2 |
| C2×#19097693 | 2 |
| C2×#19097683 | 2 |
| #23757035 | 2 |
| C2×#102×C157 | 2 |
| #1999 | 157 |