Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
424 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23765188 | C2 | semidirect |
| 5. #23764185 | C2 | semidirect |
| 6. #23761496 | C2 | semidirect |
| 7. C79×#1379 | C2 | semidirect |
| 20. #19098377 | C4 | semidirect |
| 42. #14579097 | C2×C4 | semidirect |
| 56. M32×C79 | C2×C4 | semidirect |
| 166. #1379 | D79 | semidirect |
| 167. C79 | #12940 | semidirect |
| 205. M32 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772253 | 2 |
| #23765188 | 2 |
| C2×#19098377 | 2 |
| C2×#19098365 | 2 |
| #23764185 | 2 |
| #23761496 | 2 |
| C79×#1379 | 2 |
| #12940 | 79 |