Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
390 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 69 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. #23775121 | C2 | semidirect |
| 2. #23765655 | C2 | semidirect |
| 3. #23762752 | C2 | semidirect |
| 4. #23761450 | C2 | semidirect |
| 5. #23761361 | C2 | semidirect |
| 6. #23761354 | C2 | semidirect |
| 7. C79×#2206 | C2 | semidirect |
| 88. D8×C79 | D8 | semidirect |
| 153. #2206 | D79 | semidirect |
| 158. C79 | #12319 | semidirect |
| 228. D8 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775121 | 2 |
| #23765655 | 2 |
| #23762752 | 2 |
| #23761450 | 2 |
| #23761361 | 2 |
| #23761354 | 2 |
| C79×#2206 | 2 |
| #12319 | 79 |