Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23772497 | C2 | semidirect |
| 3. #23762098 | C2 | semidirect |
| 6. #23761261 | C2 | semidirect |
| 7. C79×#1290 | C2 | semidirect |
| 165. #1290 | D79 | semidirect |
| 167. C79 | #9372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774600 | 2 |
| #23772497 | 2 |
| #23762098 | 2 |
| #23762034 | 2 |
| #23761798 | 2 |
| #23761261 | 2 |
| C79×#1290 | 2 |
| #9372 | 79 |