Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
| 4. #23764186 | C2 | semidirect |
| 5. #23761497 | C2 | semidirect |
| 6. #23761490 | C2 | semidirect |
| 25. #361×C79 | C4 | semidirect |
| 59. M32×C79 | C2×C4 | semidirect |
| 62. #108×C79 | C2×C4 | semidirect |
| 167. C79 | #12940 | semidirect |
| 183. #361 | Dic79 | semidirect |
| 205. M32 | C2×Dic79 | semidirect |
| 211. #108 | C2×Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772252 | 2 |
| #23765188 | 2 |
| C2×#19098364 | 2 |
| #23764186 | 2 |
| #23761497 | 2 |
| #23761490 | 2 |
| C2×#361×C79 | 2 |
| #12940 | 79 |