Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
582 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 105 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. #23772872 | C2 | semidirect |
| 3. #23764337 | C2 | semidirect |
| 4. #23761851 | C2 | semidirect |
| 5. #23761850 | C2 | semidirect |
| 6. #23761274 | C2 | semidirect |
| 7. C79×#3037 | C2 | semidirect |
| 121. C2×Q8×C79 | D8 | semidirect |
| 238. #3037 | D79 | semidirect |
| 243. C79 | #10255 | semidirect |
| 337. C2×Q8 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774707 | 2 |
| #23772872 | 2 |
| #23764337 | 2 |
| #23761851 | 2 |
| #23761850 | 2 |
| #23761274 | 2 |
| C79×#3037 | 2 |
| #10255 | 79 |