Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
884 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 884 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 |
|---|---|---|
| 3. #23762496 | C2 | semidirect |
| 4. #23762065 | C2 | semidirect |
| 5. #23761821 | C2 | semidirect |
| 6. C79×#3556 | C2 | semidirect |
| 17. #19098309 | C22 | semidirect |
| 18. Q8⋊(C79⋊C8) | C22 | semidirect |
| 22. #557×C79 | C22 | semidirect |
| 142. #3556 | D79 | semidirect |
| 148. C79 | #18731 | semidirect |
| 152. #557 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774338 | 2 |
| #23773776 | 2 |
| #23762496 | 2 |
| #23762065 | 2 |
| #23761821 | 2 |
| C79×#3556 | 2 |
| #18731 | 79 |