Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
542 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23764388 | C2 | semidirect |
| 4. #23762082 | C2 | semidirect |
| 6. C8×#11929608 | C2 | semidirect |
| 7. C79×#1566 | C2 | semidirect |
| 79. #11929608 | SD16 | semidirect |
| 129. C8×C79 | #100 | semidirect |
| 157. #1566 | D79 | semidirect |
| 161. C79 | #9793 | semidirect |
| 285. C8 | #14579077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098936 | 2 |
| #23764388 | 2 |
| #23764239 | 2 |
| #23762082 | 2 |
| #23762069 | 2 |
| C8×#11929608 | 2 |
| C79×#1566 | 2 |
| #9793 | 79 |