Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1068 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 179 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. #23773522 | C2 | semidirect |
| 3. #23762521 | C2 | semidirect |
| 4. #23762459 | C2 | semidirect |
| 5. #23762114 | C2 | semidirect |
| 6. #23761847 | C2 | semidirect |
| 7. C2×#559×C79 | C2 | semidirect |
| 14. #19098858 | C22 | semidirect |
| 15. #19098763 | C22 | semidirect |
| 21. Q8⋊(C79⋊C8) | C22 | semidirect |
| 165. C2×#559 | D79 | semidirect |
| 172. C79 | #18526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773850 | 2 |
| #23773522 | 2 |
| #23762521 | 2 |
| #23762459 | 2 |
| #23762114 | 2 |
| #23761847 | 2 |
| C2×#559×C79 | 2 |
| #18526 | 79 |