Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
774 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23766241 | C2 | semidirect |
| 3. #23764236 | C2 | semidirect |
| 4. #23761917 | C2 | semidirect |
| 5. #23761307 | C2 | semidirect |
| 6. #23761286 | C2 | semidirect |
| 7. C79×#1789 | C2 | semidirect |
| 8. C2×#14579186 | C4 | semidirect |
| 14. #19098564 | C4 | semidirect |
| 155. Q8×C79 | #99 | semidirect |
| 241. #1789 | D79 | semidirect |
| 245. C79 | #9368 | semidirect |
| 393. Q8 | #14579075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772652 | 2 |
| #23766241 | 2 |
| #23764236 | 2 |
| #23761917 | 2 |
| #23761307 | 2 |
| #23761286 | 2 |
| C79×#1789 | 2 |
| #9368 | 79 |