Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
798 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 251 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 |
|---|---|---|
| 4. #23763034 | C2 | direct (N × H) |
| 116. C2×C79 | #1716 | semidirect |
| 125. C79 | C2×#1716 | semidirect |
| 234. C2 | #23763034 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098959 | 2 |
| C2×#19098943 | 2 |
| C2×#19098913 | 2 |
| #23763034 | 2 |
| C2×#19098284 | 2 |
| C2×#498×C79 | 2 |
| C2×#1716 | 79 |