Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 189 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×#19097777 | C2 | semidirect |
| 3. #23757346 | C2 | semidirect |
| 4. #23757297 | C2 | semidirect |
| 5. #23757239 | C2 | semidirect |
| 6. C2×#97×C157 | C2 | semidirect |
| 39. C2×C8×C157 | D4 | semidirect |
| 79. C157 | #2932 | semidirect |
| 86. C2×#97 | D157 | semidirect |
| 117. C2×C8 | D628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097777 | 2 |
| #23757823 | 2 |
| #23757346 | 2 |
| #23757297 | 2 |
| #23757239 | 2 |
| C2×#97×C157 | 2 |
| #2932 | 157 |