Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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×C4×Dic314 | C2 | semidirect |
| 2. #23757584 | C2 | semidirect |
| 3. #23757565 | C2 | semidirect |
| 4. #23757470 | C2 | semidirect |
| 5. #23757411 | C2 | semidirect |
| 6. #23757373 | C2 | semidirect |
| 7. #23757330 | C2 | semidirect |
| 66. Dic314 | #41 | semidirect |
| 111. C157 | #3112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic314 | 2 |
| #23757584 | 2 |
| #23757565 | 2 |
| #23757470 | 2 |
| #23757411 | 2 |
| #23757373 | 2 |
| #23757330 | 2 |
| #532×C157 | 2 |
| #3112 | 157 |