Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
552 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 145 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×#19097803 | C2 | semidirect |
| 3. C4⋊Q8×D157 | C2 | semidirect |
| 4. #23757666 | C2 | semidirect |
| 5. #23757652 | C2 | semidirect |
| 6. #23757647 | C2 | semidirect |
| 7. #23757646 | C2 | semidirect |
| 8. C4×#14578937 | C2 | semidirect |
| 9. #494×C157 | C2 | semidirect |
| 46. #14578937 | D4 | semidirect |
| 89. C4×C157 | #137 | semidirect |
| 98. C157 | #3152 | semidirect |
| 105. #494 | D157 | semidirect |
| 191. C4 | #19097803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097803 | 2 |
| #23757824 | 2 |
| C4⋊Q8×D157 | 2 |
| #23757666 | 2 |
| #23757652 | 2 |
| #23757647 | 2 |
| #23757646 | 2 |
| C4×#14578937 | 2 |
| #494×C157 | 2 |
| #3152 | 157 |