Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
934 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 159 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×#19098940 | C2 | semidirect |
| 2. C2×#19098939 | C2 | semidirect |
| 3. #23764205 | C2 | semidirect |
| 4. C79⋊#1273 | C2 | semidirect |
| 5. C79×#1957 | C2 | semidirect |
| 63. C2×C79⋊C8 | D8 | semidirect |
| 78. C2×C8×C79 | D8 | semidirect |
| 152. #1957 | D79 | semidirect |
| 154. C79 | #10304 | semidirect |
| 227. C2×C8 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098940 | 2 |
| C2×#19098939 | 2 |
| #23764205 | 2 |
| C79⋊#1273 | 2 |
| C79×#1957 | 2 |
| #10304 | 79 |