Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
554 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 139 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. #23764228 | C2 | semidirect |
| 3. #23762159 | C2 | semidirect |
| 4. #23761852 | C2 | semidirect |
| 5. C42×C8×C79 | C2 | semidirect |
| 7. #19098968 | C4 | semidirect |
| 8. #19098940 | C4 | semidirect |
| 9. #19098910 | C4 | semidirect |
| 74. C42×C79 | D8 | semidirect |
| 104. C8×C79 | #104 | semidirect |
| 130. C42×C8 | D79 | semidirect |
| 133. C79 | #9844 | semidirect |
| 202. C42 | D632 | semidirect |
| 233. C8 | #14579089 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773979 | 2 |
| #23764228 | 2 |
| #23762159 | 2 |
| #23761852 | 2 |
| C42×C8×C79 | 2 |
| #9844 | 79 |