Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
528 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23773207 | C2 | semidirect |
| 4. #23764335 | C2 | semidirect |
| 5. #23761854 | C2 | semidirect |
| 7. C79×#1292 | C2 | semidirect |
| 96. C2×Dic158 | SD16 | semidirect |
| 223. #1292 | D79 | semidirect |
| 224. C79 | #10257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774717 | 2 |
| #23773207 | 2 |
| #23772874 | 2 |
| #23764335 | 2 |
| #23761854 | 2 |
| #23761850 | 2 |
| C79×#1292 | 2 |
| #10257 | 79 |