Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
478 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23764372 | C2 | semidirect |
| 4. #23762080 | C2 | semidirect |
| 5. #23761258 | C2 | semidirect |
| 6. #23761230 | C2 | semidirect |
| 10. #19098959 | C4 | semidirect |
| 11. #19098909 | C4 | semidirect |
| 181. C79 | #9287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774525 | 2 |
| #23772118 | 2 |
| #23764372 | 2 |
| #23762080 | 2 |
| #23761258 | 2 |
| #23761230 | 2 |
| C79×#1517 | 2 |
| #9287 | 79 |