Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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. C4×#14579096 | C2 | semidirect |
| 3. #23762161 | C2 | semidirect |
| 6. #23761271 | C2 | semidirect |
| 7. C79×#1291 | C2 | semidirect |
| 173. #1291 | D79 | semidirect |
| 174. C79 | #8693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772369 | 2 |
| C4×#14579096 | 2 |
| #23762161 | 2 |
| #23762008 | 2 |
| #23762005 | 2 |
| #23761271 | 2 |
| C79×#1291 | 2 |
| #8693 | 79 |