Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
552 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 3. #23763427 | C2 | semidirect |
| 4. #23763178 | C2 | semidirect |
| 5. #23761972 | C2 | semidirect |
| 7. C79×#1996 | C2 | semidirect |
| 8. C22×#11929611 | C4 | semidirect |
| 16. C2×#14579092 | C4 | semidirect |
| 17. C2×#14579085 | C4 | semidirect |
| 18. C2×#14579081 | C4 | semidirect |
| 194. C79⋊C8 | #99 | semidirect |
| 233. #1996 | D79 | semidirect |
| 239. C79 | #9786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098794 | 2 |
| #23764236 | 2 |
| #23763427 | 2 |
| #23763178 | 2 |
| #23761972 | 2 |
| #23761967 | 2 |
| C79×#1996 | 2 |
| #9786 | 79 |