Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
520 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 2. #23773051 | C2 | semidirect |
| 3. C2×#19098379 | C2 | semidirect |
| 4. #23765136 | C2 | semidirect |
| 5. #23765029 | C2 | semidirect |
| 6. #23761515 | C2 | semidirect |
| 7. C2×#510×C79 | C2 | semidirect |
| 206. C2×#510 | D79 | semidirect |
| 213. C79 | #13311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773116 | 2 |
| #23773051 | 2 |
| C2×#19098379 | 2 |
| #23765136 | 2 |
| #23765029 | 2 |
| #23761515 | 2 |
| C2×#510×C79 | 2 |
| #13311 | 79 |