Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
592 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#19097696 | C2 | semidirect |
| 3. C2×#19097695 | C2 | semidirect |
| 4. C2×#19097694 | C2 | semidirect |
| 7. C2×#103×C157 | C2 | semidirect |
| 15. C2×Q8×D157 | C4 | semidirect |
| 87. Dic314 | C22⋊C4 | semidirect |
| 107. Q8×C157 | C22⋊C4 | semidirect |
| 134. C2×D157 | #103 | semidirect |
| 152. C157 | #1787 | semidirect |
| 158. C2×#103 | D157 | semidirect |
| 245. Q8 | #14578931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D157 | 2 |
| C2×#19097696 | 2 |
| C2×#19097695 | 2 |
| C2×#19097694 | 2 |
| C2×#19097683 | 2 |
| #23757130 | 2 |
| C2×#103×C157 | 2 |
| #1787 | 157 |