Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
380 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 79 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. #23764957 | C2 | semidirect |
| 4. #23761226 | C2 | semidirect |
| 5. #23761222 | C2 | semidirect |
| 7. C79×#2072 | C2 | semidirect |
| 187. #2072 | D79 | semidirect |
| 192. C79 | #7811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771382 | 2 |
| #23764957 | 2 |
| #23764804 | 2 |
| #23761226 | 2 |
| #23761222 | 2 |
| #23761220 | 2 |
| C79×#2072 | 2 |
| #7811 | 79 |