Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
546 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 167 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. #23772011 | C2 | semidirect |
| 2. #23765617 | C2 | semidirect |
| 3. #23765612 | C2 | semidirect |
| 4. C2×#19098385 | C2 | semidirect |
| 5. #23765149 | C2 | semidirect |
| 6. #23765021 | C2 | semidirect |
| 152. C79 | #33659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772011 | 2 |
| #23765617 | 2 |
| #23765612 | 2 |
| C2×#19098385 | 2 |
| #23765149 | 2 |
| #23765021 | 2 |
| C79×#3060 | 2 |
| #33659 | 79 |