Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
530 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23766213 | C2 | semidirect |
| 3. #23761997 | C2 | semidirect |
| 4. #23761947 | C2 | semidirect |
| 5. #23761265 | C2 | semidirect |
| 6. #23761256 | C2 | semidirect |
| 7. C79×#1980 | C2 | semidirect |
| 9. #19098950 | C4 | semidirect |
| 10. #19098925 | C4 | semidirect |
| 54. #14579072 | C2×C4 | semidirect |
| 63. C4⋊Q8×C79 | C2×C4 | semidirect |
| 64. #127×C79 | C2×C4 | semidirect |
| 224. #1980 | D79 | semidirect |
| 229. C79 | #9381 | semidirect |
| 260. C4⋊Q8 | C4×D79 | semidirect |
| 261. #127 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774383 | 2 |
| #23766213 | 2 |
| #23761997 | 2 |
| #23761947 | 2 |
| #23761265 | 2 |
| #23761256 | 2 |
| C79×#1980 | 2 |
| #9381 | 79 |