Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
258 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 73 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. #23757247 | C2 | semidirect |
| 2. #23757068 | C2 | semidirect |
| 3. #23757066 | C2 | semidirect |
| 8. C2×#41×C157 | C4 | semidirect |
| 10. C4⋊Q8×C157 | C4 | semidirect |
| 12. #124×C157 | C4 | semidirect |
| 16. C2×C42×C157 | C4 | semidirect |
| 85. C157 | #2126 | semidirect |
| 91. C2×#41 | Dic157 | semidirect |
| 93. C4⋊Q8 | Dic157 | semidirect |
| 95. #124 | Dic157 | semidirect |
| 100. C2×C42 | Dic157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757247 | 2 |
| #23757068 | 2 |
| #23757066 | 2 |
| #532×C157 | 2 |
| #2126 | 157 |