Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
466 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 111 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×#19098377 | C2 | semidirect |
| 3. #23765137 | C2 | semidirect |
| 4. #23765129 | C2 | semidirect |
| 5. #23765117 | C2 | semidirect |
| 6. #23763524 | C2 | semidirect |
| 7. C79×#2110 | C2 | semidirect |
| 13. #19098947 | C4 | semidirect |
| 14. #19098940 | C4 | semidirect |
| 62. M32×C79 | D4 | semidirect |
| 64. C2×C16×C79 | D4 | semidirect |
| 180. #2110 | D79 | semidirect |
| 182. C79 | #13215 | semidirect |
| 233. M32 | D316 | semidirect |
| 235. C2×C16 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773886 | 2 |
| C2×#19098377 | 2 |
| #23765137 | 2 |
| #23765129 | 2 |
| #23765117 | 2 |
| #23763524 | 2 |
| C79×#2110 | 2 |
| #13215 | 79 |