Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
396 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23765585 | C2 | semidirect |
| 3. #23761408 | C2 | semidirect |
| 4. #23761324 | C2 | semidirect |
| 5. C79×#2076 | C2 | semidirect |
| 13. C22⋊(C79⋊C16) | C22 | semidirect |
| 14. C2×#107×C79 | C22 | semidirect |
| 18. #340×C79 | C22 | semidirect |
| 144. #2076 | D79 | semidirect |
| 147. C79 | #12281 | semidirect |
| 153. C2×#107 | C2×D79 | semidirect |
| 160. #340 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774151 | 2 |
| #23765585 | 2 |
| #23761408 | 2 |
| #23761324 | 2 |
| C79×#2076 | 2 |
| #12281 | 79 |