Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
404 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23762158 | C2 | semidirect |
| 3. #23762155 | C2 | semidirect |
| 5. C79⋊#1309 | C2 | semidirect |
| 6. C79⋊#1309 | C2 | semidirect |
| 164. C79 | #8640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772112 | 2 |
| #23762158 | 2 |
| #23762155 | 2 |
| #23762135 | 2 |
| C79⋊#1309 | 2 |
| C79×#1560 | 2 |
| #8640 | 79 |