Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
458 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23763605 | C2 | semidirect |
| 4. #23761288 | C2 | semidirect |
| 117. C2×C4×C79 | #108 | semidirect |
| 161. C79 | #8860 | semidirect |
| 273. C2×C4 | #14579096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772441 | 2 |
| #23763605 | 2 |
| #23761718 | 2 |
| #23761288 | 2 |
| C79×#1870 | 2 |
| #8860 | 79 |