Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
210 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 210 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 |
|---|---|---|
| 1. C2×#19098398 | C2 | semidirect |
| 2. C2×#19098397 | C2 | semidirect |
| 3. #23765486 | C2 | semidirect |
| 4. #23761601 | C2 | semidirect |
| 5. #23761578 | C2 | semidirect |
| 6. #23761577 | C2 | semidirect |
| 7. C79×#2215 | C2 | semidirect |
| 28. C79⋊C32 | D4 | semidirect |
| 103. #2215 | D79 | semidirect |
| 107. C79 | #13697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098398 | 2 |
| C2×#19098397 | 2 |
| #23765486 | 2 |
| #23761601 | 2 |
| #23761578 | 2 |
| #23761577 | 2 |
| C79×#2215 | 2 |
| #13697 | 79 |