Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
452 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 127 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. #23776550 | C2 | semidirect |
| 2. #23765717 | C2 | semidirect |
| 3. #23765716 | C2 | semidirect |
| 4. #23765706 | C2 | semidirect |
| 5. C2×Dic1264 | C2 | semidirect |
| 6. Q64×D79 | C2 | semidirect |
| 7. #23765693 | C2 | semidirect |
| 8. C79×#2262 | C2 | semidirect |
| 108. #2262 | D79 | semidirect |
| 112. C79 | #33984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776550 | 2 |
| #23765717 | 2 |
| #23765716 | 2 |
| #23765706 | 2 |
| C2×Dic1264 | 2 |
| Q64×D79 | 2 |
| #23765693 | 2 |
| C79×#2262 | 2 |
| #33984 | 79 |