Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23766148 | C2 | semidirect |
| 4. #23762080 | C2 | semidirect |
| 6. #23761259 | C2 | semidirect |
| 7. C79×#1274 | C2 | semidirect |
| 10. #19098936 | C4 | semidirect |
| 11. #19098914 | C4 | semidirect |
| 108. C42×C79 | SD16 | semidirect |
| 189. #1274 | D79 | semidirect |
| 190. C79 | #9301 | semidirect |
| 291. C42 | #11929613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774327 | 2 |
| #23766148 | 2 |
| #23764232 | 2 |
| #23762080 | 2 |
| #23761961 | 2 |
| #23761259 | 2 |
| C79×#1274 | 2 |
| #9301 | 79 |