Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
302 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 81 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. M64×D79 | C2 | semidirect |
| 3. #367×D79 | C2 | semidirect |
| 4. #23761588 | C2 | semidirect |
| 5. #23761587 | C2 | semidirect |
| 6. #23761586 | C2 | semidirect |
| 7. C79×#1418 | C2 | semidirect |
| 9. #19098996 | C4 | semidirect |
| 13. #19098992 | C4 | semidirect |
| 14. Q32×D79 | C4 | semidirect |
| 16. D16×D79 | C4 | semidirect |
| 19. #19098397 | C22 | semidirect |
| 22. #19098391 | C22 | semidirect |
| 25. M64×C79 | C22 | semidirect |
| 26. #367×C79 | C22 | semidirect |
| 38. Dic632 | C2×C4 | semidirect |
| 43. D1264 | C2×C4 | semidirect |
| 54. Q32×C79 | C2×C4 | semidirect |
| 56. D16×C79 | C2×C4 | semidirect |
| 146. D79 | #1418 | direct (N × H) |
| 153. #1418 | D79 | direct (N × H) |
| 154. C79 | C2×#1418 | semidirect |
| 169. M64 | C2×D79 | semidirect |
| 173. #367 | C2×D79 | semidirect |
| 188. Q32 | C4×D79 | semidirect |
| 195. D16 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #508×D79 | 2 |
| M64×D79 | 2 |
| #367×D79 | 2 |
| #23761588 | 2 |
| #23761587 | 2 |
| #23761586 | 2 |
| C79×#1418 | 2 |
| C2×#1418 | 79 |