Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23772317 | C2 | semidirect |
| 2. #23765149 | C2 | semidirect |
| 3. C2×#19098376 | C2 | semidirect |
| 4. #23764311 | C2 | semidirect |
| 5. #23761512 | C2 | semidirect |
| 6. #23761487 | C2 | semidirect |
| 24. #509×C79 | C4 | semidirect |
| 179. C79 | #13032 | semidirect |
| 184. #509 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772317 | 2 |
| #23765149 | 2 |
| C2×#19098376 | 2 |
| #23764311 | 2 |
| #23761512 | 2 |
| #23761487 | 2 |
| C2×#509×C79 | 2 |
| #13032 | 79 |