Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
258 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23762194 | C2 | semidirect |
| 3. #23761360 | C2 | semidirect |
| 4. C16×C79⋊C8 | C2 | semidirect |
| 5. C79×#1371 | C2 | semidirect |
| 19. D1264 | C8 | semidirect |
| 33. D632 | C2×C8 | semidirect |
| 46. C16×C79 | C2×C8 | semidirect |
| 62. C79⋊C8 | D16 | semidirect |
| 80. #1371 | D79 | semidirect |
| 83. C79 | C8×D16 | semidirect |
| 124. C16 | C8×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D1264 | 2 |
| #23762194 | 2 |
| #23761360 | 2 |
| C16×C79⋊C8 | 2 |
| C79×#1371 | 2 |
| C8×D16 | 79 |