Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
288 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 63 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×#19098403 | C2 | semidirect |
| 3. C2×#19098400 | C2 | semidirect |
| 4. #23761580 | C2 | semidirect |
| 5. #23761577 | C2 | semidirect |
| 6. C22⋊(C79⋊C32) | C2 | semidirect |
| 7. C79×#2216 | C2 | semidirect |
| 114. #2216 | D79 | semidirect |
| 118. C79 | #13666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098995 | 2 |
| C2×#19098403 | 2 |
| C2×#19098400 | 2 |
| #23761580 | 2 |
| #23761577 | 2 |
| C22⋊(C79⋊C32) | 2 |
| C79×#2216 | 2 |
| #13666 | 79 |