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. #23762032 | C2 | semidirect |
| 3. #23761978 | C2 | semidirect |
| 4. #23761951 | C2 | semidirect |
| 5. #23761948 | C2 | semidirect |
| 6. #23761870 | C2 | semidirect |
| 7. C79×#1554 | C2 | semidirect |
| 10. #19099298 | C4 | semidirect |
| 11. #19099291 | C4 | semidirect |
| 13. #19099235 | C4 | semidirect |
| 14. Q8×D316 | C4 | semidirect |
| 266. #1554 | 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 |
|---|---|
| #23777871 | 2 |
| #23762032 | 2 |
| #23761978 | 2 |
| #23761951 | 2 |
| #23761948 | 2 |
| #23761870 | 2 |
| C79×#1554 | 2 |
| #8503 | 79 |