Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
942 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 942 conjugacy classes of subgroups — too many to draw. Only its 155 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. #23777800 | C2 | semidirect |
| 2. #23774391 | C2 | semidirect |
| 3. #23762721 | C2 | semidirect |
| 4. #23762692 | C2 | semidirect |
| 5. #23762038 | C2 | semidirect |
| 6. #23762010 | C2 | semidirect |
| 7. C79×#3135 | C2 | semidirect |
| 165. #3135 | D79 | semidirect |
| 170. C79 | #19061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777800 | 2 |
| #23774391 | 2 |
| #23762721 | 2 |
| #23762692 | 2 |
| #23762038 | 2 |
| #23762010 | 2 |
| C79×#3135 | 2 |
| #19061 | 79 |