Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#19098375 | C2 | semidirect |
| 3. #23765112 | C2 | semidirect |
| 4. C2×#19098365 | C2 | semidirect |
| 5. #23764186 | C2 | semidirect |
| 6. #23761488 | C2 | semidirect |
| 7. C2×#359×C79 | C2 | semidirect |
| 69. #108×C79 | D4 | semidirect |
| 192. C2×#359 | D79 | semidirect |
| 197. C79 | #13411 | semidirect |
| 253. #108 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773887 | 2 |
| C2×#19098375 | 2 |
| #23765112 | 2 |
| C2×#19098365 | 2 |
| #23764186 | 2 |
| #23761488 | 2 |
| C2×#359×C79 | 2 |
| #13411 | 79 |