Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
736 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 147 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. #23761523 | C2 | semidirect |
| 4. #23761522 | C2 | semidirect |
| 5. C79×#1392 | C2 | semidirect |
| 213. #1392 | D79 | semidirect |
| 214. C79 | #12579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #413×D79 | 2 |
| #23771842 | 2 |
| #23761523 | 2 |
| #23761522 | 2 |
| C79×#1392 | 2 |
| #12579 | 79 |