Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
868 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 868 conjugacy classes of subgroups — too many to draw. Only its 179 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. #23764203 | C2 | semidirect |
| 2. #23763400 | C2 | semidirect |
| 3. C2×#19098312 | C2 | semidirect |
| 4. C2×D4⋊(C79⋊C8) | C2 | semidirect |
| 16. #555×C79 | C4 | semidirect |
| 171. C79 | #8452 | semidirect |
| 174. #555 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764203 | 2 |
| #23763400 | 2 |
| C2×#19098312 | 2 |
| C2×D4⋊(C79⋊C8) | 2 |
| C2×#555×C79 | 2 |
| #8452 | 79 |