Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
346 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23763540 | C2 | semidirect |
| 5. #23761258 | C2 | semidirect |
| 6. #23761244 | C2 | semidirect |
| 7. C79×#1286 | C2 | semidirect |
| 153. #1286 | D79 | semidirect |
| 155. C79 | #10634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764223 | 2 |
| #23763540 | 2 |
| #23762069 | 2 |
| #23762067 | 2 |
| #23761258 | 2 |
| #23761244 | 2 |
| C79×#1286 | 2 |
| #10634 | 79 |