Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
584 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 105 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. #23773432 | C2 | semidirect |
| 3. #23764340 | C2 | semidirect |
| 4. #23761800 | C2 | semidirect |
| 5. C79×#1275 | C2 | semidirect |
| 84. C2×C8×C79 | SD16 | semidirect |
| 140. #1275 | D79 | semidirect |
| 141. C79 | #10034 | semidirect |
| 212. C2×C8 | #11929613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773846 | 2 |
| #23773432 | 2 |
| #23764340 | 2 |
| #23761800 | 2 |
| C79×#1275 | 2 |
| #10034 | 79 |