Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
994 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 283 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. C2×#19098961 | C2 | semidirect |
| 2. C2×#19098959 | C2 | semidirect |
| 4. #23762986 | C2 | direct (N × H) |
| 5. C2×C8×C79⋊C8 | C2 | semidirect |
| 10. #19098961 | C22 | semidirect |
| 12. #19098959 | C22 | semidirect |
| 18. C8×C79⋊C8 | C22 | semidirect |
| 60. C2×C79⋊C8 | SD16 | semidirect |
| 80. C2×C8×C79 | SD16 | semidirect |
| 109. C8×C79 | C2×SD16 | semidirect |
| 110. C79⋊C8 | C2×SD16 | semidirect |
| 125. C2×C79 | #1705 | semidirect |
| 134. C79 | C2×#1705 | semidirect |
| 204. C2×C8 | #11929612 | semidirect |
| 238. C8 | C2×#11929612 | semidirect |
| 252. C2 | #23762986 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098961 | 2 |
| C2×#19098959 | 2 |
| C2×#19098935 | 2 |
| #23762986 | 2 |
| C2×C8×C79⋊C8 | 2 |
| C2×#492×C79 | 2 |
| C2×#1705 | 79 |