Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 75 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. #23761572 | C2 | direct (N × H) |
| 125. C2×C79 | #1413 | semidirect |
| 131. C79 | C2×#1413 | semidirect |
| 251. C2 | #23761572 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098931 | 2 |
| C2×#19098362 | 2 |
| #23761572 | 2 |
| C2×#356×C79 | 2 |
| C2×#1413 | 79 |