Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
672 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 672 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. #23762108 | C2 | semidirect |
| 3. #23762029 | C2 | semidirect |
| 4. #23761978 | C2 | semidirect |
| 5. #23761952 | C2 | semidirect |
| 6. #23761947 | C2 | semidirect |
| 7. C79×#1496 | C2 | semidirect |
| 9. #19099299 | C4 | semidirect |
| 11. #19099288 | C4 | semidirect |
| 13. #19099233 | C4 | semidirect |
| 14. #19099228 | C4 | semidirect |
| 271. #1496 | D79 | semidirect |
| 272. C79 | #8503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777865 | 2 |
| #23762108 | 2 |
| #23762029 | 2 |
| #23761978 | 2 |
| #23761952 | 2 |
| #23761947 | 2 |
| C79×#1496 | 2 |
| #8503 | 79 |