Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
610 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 610 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 |
|---|---|---|
| 1. #23764241 | C2 | semidirect |
| 2. #23762159 | C2 | semidirect |
| 3. #23762068 | C2 | semidirect |
| 4. C8×#11929608 | C2 | semidirect |
| 47. #11929608 | D8 | semidirect |
| 97. C8×C79 | #100 | semidirect |
| 127. C79 | #9802 | semidirect |
| 222. C8 | #14579078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764241 | 2 |
| #23762159 | 2 |
| #23762068 | 2 |
| C8×#11929608 | 2 |
| C2×#493×C79 | 2 |
| #9802 | 79 |