Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
690 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23772428 | C2 | semidirect |
| 3. #23762114 | C2 | semidirect |
| 4. #23761740 | C2 | semidirect |
| 5. #23761257 | C2 | semidirect |
| 6. #23761255 | C2 | semidirect |
| 7. C79×#1555 | C2 | semidirect |
| 51. C4⋊(C79⋊C8) | D4 | semidirect |
| 68. C4⋊C8×C79 | D4 | semidirect |
| 225. #1555 | D79 | semidirect |
| 229. C79 | #9457 | semidirect |
| 283. C4⋊C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772428 | 2 |
| #23768347 | 2 |
| #23762114 | 2 |
| #23761740 | 2 |
| #23761257 | 2 |
| #23761255 | 2 |
| C79×#1555 | 2 |
| #9457 | 79 |