Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
238 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23762206 | C2 | semidirect |
| 4. #23761471 | C2 | semidirect |
| 5. #23761365 | C2 | semidirect |
| 6. #23761316 | C2 | semidirect |
| 26. #14579105 | C8 | semidirect |
| 46. Dic316 | C2×C8 | semidirect |
| 56. C79⋊C16 | C2×C8 | semidirect |
| 113. C79 | #12043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579105 | 2 |
| #23762206 | 2 |
| D8×C79⋊C8 | 2 |
| #23761471 | 2 |
| #23761365 | 2 |
| #23761316 | 2 |
| C79×#1331 | 2 |
| #12043 | 79 |