Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
636 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#19098882 | C2 | semidirect |
| 3. #23767892 | C2 | semidirect |
| 4. #23764236 | C2 | semidirect |
| 5. #23763491 | C2 | semidirect |
| 6. #23761969 | C2 | semidirect |
| 7. C79×#1282 | C2 | semidirect |
| 228. #1282 | D79 | semidirect |
| 229. C79 | #9950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774151 | 2 |
| C2×#19098882 | 2 |
| #23767892 | 2 |
| #23764236 | 2 |
| #23763491 | 2 |
| #23761969 | 2 |
| C79×#1282 | 2 |
| #9950 | 79 |