Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
552 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#19097802 | C2 | semidirect |
| 3. #23757665 | C2 | semidirect |
| 4. #23757652 | C2 | semidirect |
| 5. #23757647 | C2 | semidirect |
| 6. C4×#14578938 | C2 | semidirect |
| 7. C2×C4⋊Q8×C157 | C2 | semidirect |
| 34. #14578938 | D4 | semidirect |
| 76. C4×C157 | #137 | semidirect |
| 83. C157 | #3152 | semidirect |
| 87. C2×C4⋊Q8 | D157 | semidirect |
| 161. C4 | #19097802 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097802 | 2 |
| #23757823 | 2 |
| #23757665 | 2 |
| #23757652 | 2 |
| #23757647 | 2 |
| C4×#14578938 | 2 |
| C2×C4⋊Q8×C157 | 2 |
| #3152 | 157 |