Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1722 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1722 conjugacy classes of subgroups — too many to draw. Only its 219 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. C2×#19098850 | C2 | semidirect |
| 3. #23762514 | C2 | direct (N × H) |
| 4. C2×#19098307 | C2 | semidirect |
| 5. C2×#19098292 | C2 | semidirect |
| 6. C2×#492×C79 | C2 | semidirect |
| 15. #19098850 | C22 | semidirect |
| 17. C2×C4⋊(C79⋊C8) | C22 | semidirect |
| 19. #19098307 | C22 | semidirect |
| 20. #19098292 | C22 | semidirect |
| 22. C2×C4⋊Q8×C79 | C22 | semidirect |
| 25. #492×C79 | C22 | semidirect |
| 26. C2×C4×C8×C79 | C22 | semidirect |
| 49. C4⋊(C79⋊C8) | C23 | semidirect |
| 59. C4⋊Q8×C79 | C23 | semidirect |
| 66. C4×C8×C79 | C23 | semidirect |
| 73. C2×D316 | SD16 | semidirect |
| 146. D316 | C2×SD16 | semidirect |
| 172. C2×C79 | #1629 | semidirect |
| 177. C2×#492 | D79 | semidirect |
| 182. C79 | C2×#1629 | semidirect |
| 188. C2×C4⋊Q8 | C2×D79 | semidirect |
| 194. #492 | C2×D79 | semidirect |
| 200. C2×C4×C8 | C2×D79 | semidirect |
| 220. C4⋊Q8 | C22×D79 | semidirect |
| 242. C4×C8 | C22×D79 | semidirect |
| 348. C2 | #23762514 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099198 | 2 |
| C2×#19098850 | 2 |
| #23762514 | 2 |
| C2×#19098307 | 2 |
| C2×#19098292 | 2 |
| C2×#492×C79 | 2 |
| C2×#1629 | 79 |