Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
422 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 1. #23770529 | C2 | semidirect |
| 4. #23761423 | C2 | semidirect |
| 5. #23761420 | C2 | semidirect |
| 6. #23761348 | C2 | semidirect |
| 108. C22⋊C4×C79 | SD16 | semidirect |
| 204. C79 | #12178 | semidirect |
| 304. C22⋊C4 | #11929612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23770529 | 2 |
| #23762420 | 2 |
| #23762352 | 2 |
| #23761423 | 2 |
| #23761420 | 2 |
| #23761348 | 2 |
| C79×#2044 | 2 |
| #12178 | 79 |