Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
476 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #23764262 | C2 | semidirect |
| 5. #23761510 | C2 | semidirect |
| 6. #23761481 | C2 | semidirect |
| 7. C2×#362×C79 | C2 | semidirect |
| 11. #19099004 | C4 | semidirect |
| 180. C2×#362 | D79 | semidirect |
| 185. C79 | #13028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099004 | 2 |
| C2×#19098679 | 2 |
| #23765113 | 2 |
| #23764262 | 2 |
| #23761510 | 2 |
| #23761481 | 2 |
| C2×#362×C79 | 2 |
| #13028 | 79 |