Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
594 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23764236 | C2 | semidirect |
| 3. #23763425 | C2 | semidirect |
| 4. #23761969 | C2 | semidirect |
| 5. C79×#1752 | C2 | semidirect |
| 6. C22×D632 | C4 | semidirect |
| 12. C2×#14579095 | C4 | semidirect |
| 14. C2×#14579083 | C4 | semidirect |
| 146. C8×C79 | #99 | semidirect |
| 181. #1752 | D79 | semidirect |
| 183. C79 | #9785 | semidirect |
| 324. C8 | #14579075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098799 | 2 |
| #23764236 | 2 |
| #23763425 | 2 |
| #23761969 | 2 |
| C79×#1752 | 2 |
| #9785 | 79 |