Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
814 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 1. #23773960 | C2 | semidirect |
| 3. #23763002 | C2 | semidirect |
| 4. #23762998 | C2 | semidirect |
| 5. #23762993 | C2 | semidirect |
| 6. #23762988 | C2 | semidirect |
| 7. C2×C8×C79⋊C8 | C2 | semidirect |
| 8. C79×#3160 | C2 | semidirect |
| 79. C2×C8×C79 | SD16 | semidirect |
| 109. C79⋊C8 | #135 | semidirect |
| 127. #3160 | D79 | semidirect |
| 134. C79 | #19596 | semidirect |
| 203. C2×C8 | #11929611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773960 | 2 |
| #23773828 | 2 |
| #23763002 | 2 |
| #23762998 | 2 |
| #23762993 | 2 |
| #23762988 | 2 |
| C2×C8×C79⋊C8 | 2 |
| C79×#3160 | 2 |
| #19596 | 79 |