Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
494 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 494 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 |
|---|---|---|
| 3. #23764220 | C2 | semidirect |
| 4. #23762071 | C2 | semidirect |
| 6. #23761259 | C2 | semidirect |
| 7. C79×#1275 | C2 | semidirect |
| 11. #19098968 | C4 | semidirect |
| 12. #19098910 | C4 | semidirect |
| 188. #1275 | D79 | semidirect |
| 189. C79 | #9291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774523 | 2 |
| #23772119 | 2 |
| #23764220 | 2 |
| #23762071 | 2 |
| #23761961 | 2 |
| #23761259 | 2 |
| C79×#1275 | 2 |
| #9291 | 79 |