Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
534 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. C2×#19098379 | C2 | semidirect |
| 5. #23764316 | C2 | semidirect |
| 6. #23761488 | C2 | semidirect |
| 7. C22×Q32×C79 | C2 | semidirect |
| 197. C22×Q32 | D79 | semidirect |
| 203. C79 | #13339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099004 | 2 |
| #23773889 | 2 |
| C2×#19098379 | 2 |
| C2×#19098371 | 2 |
| #23764316 | 2 |
| #23761488 | 2 |
| C22×Q32×C79 | 2 |
| #13339 | 79 |