Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
348 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 61 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. #23765598 | C2 | semidirect |
| 3. #23765578 | C2 | semidirect |
| 4. #23764825 | C2 | semidirect |
| 5. #23761411 | C2 | semidirect |
| 6. #23761323 | C2 | semidirect |
| 7. C79×#1347 | C2 | semidirect |
| 174. #1347 | D79 | semidirect |
| 176. C79 | #12280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774187 | 2 |
| #23765598 | 2 |
| #23765578 | 2 |
| #23764825 | 2 |
| #23761411 | 2 |
| #23761323 | 2 |
| C79×#1347 | 2 |
| #12280 | 79 |