Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1026 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23764199 | C2 | semidirect |
| 3. #23762096 | C2 | semidirect |
| 4. #23762012 | C2 | semidirect |
| 5. C79×#1466 | C2 | semidirect |
| 14. C2×C4⋊(C79⋊C8) | C22 | semidirect |
| 16. C2×#14579072 | C22 | semidirect |
| 21. #432×C79 | C22 | semidirect |
| 173. #1466 | D79 | semidirect |
| 174. C79 | #8456 | semidirect |
| 184. #432 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777164 | 2 |
| #23764199 | 2 |
| #23762096 | 2 |
| #23762012 | 2 |
| C79×#1466 | 2 |
| #8456 | 79 |