Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
494 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23764245 | C2 | semidirect |
| 3. #23762159 | C2 | semidirect |
| 4. #23762072 | C2 | semidirect |
| 6. C8×#11929608 | C2 | semidirect |
| 161. C79 | #9796 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764245 | 2 |
| #23764241 | 2 |
| #23762159 | 2 |
| #23762072 | 2 |
| #23762068 | 2 |
| C8×#11929608 | 2 |
| C2×#486×C79 | 2 |
| #9796 | 79 |