Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
800 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23764376 | C2 | semidirect |
| 3. #23764229 | C2 | semidirect |
| 4. #23764227 | C2 | semidirect |
| 5. #23762137 | C2 | semidirect |
| 6. #23762133 | C2 | semidirect |
| 7. C79×#1560 | C2 | semidirect |
| 8. #19099307 | C4 | semidirect |
| 247. #1560 | D79 | semidirect |
| 248. C79 | #8532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777798 | 2 |
| #23764376 | 2 |
| #23764229 | 2 |
| #23764227 | 2 |
| #23762137 | 2 |
| #23762133 | 2 |
| C79×#1560 | 2 |
| #8532 | 79 |