Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
304 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 87 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. #23762191 | C2 | semidirect |
| 5. #23761693 | C2 | semidirect |
| 6. #23761238 | C2 | semidirect |
| 7. C79×#1299 | C2 | semidirect |
| 154. #1299 | D79 | semidirect |
| 156. C79 | #9588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23762191 | 2 |
| #23762060 | 2 |
| #23761850 | 2 |
| #23761818 | 2 |
| #23761693 | 2 |
| #23761238 | 2 |
| C79×#1299 | 2 |
| #9588 | 79 |