Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
398 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23772505 | C2 | semidirect |
| 3. #23762111 | C2 | semidirect |
| 6. #23761263 | C2 | semidirect |
| 7. C79×#1308 | C2 | semidirect |
| 159. #1308 | D79 | semidirect |
| 161. C79 | #9334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774405 | 2 |
| #23772505 | 2 |
| #23762111 | 2 |
| #23762023 | 2 |
| #23761753 | 2 |
| #23761263 | 2 |
| C79×#1308 | 2 |
| #9334 | 79 |