Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
528 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23773922 | C2 | semidirect |
| 5. #23761802 | C2 | semidirect |
| 6. #23761230 | C2 | semidirect |
| 7. C79×#1481 | C2 | semidirect |
| 99. C2×C79⋊C8 | SD16 | semidirect |
| 201. #1481 | D79 | semidirect |
| 203. C79 | #10036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773922 | 2 |
| #23773409 | 2 |
| #23773404 | 2 |
| #23764197 | 2 |
| #23761802 | 2 |
| #23761230 | 2 |
| C79×#1481 | 2 |
| #10036 | 79 |