Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
776 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 776 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. #23761421 | C2 | direct (N × H) |
| 11. C23×Q8×C79 | C4 | semidirect |
| 16. #393×C79 | C4 | semidirect |
| 19. C2×#95×C79 | C4 | semidirect |
| 33. C22×Q8×C79 | C2×C4 | semidirect |
| 50. #95×C79 | C2×C4 | semidirect |
| 203. C2×C79 | #1351 | semidirect |
| 211. C79 | C2×#1351 | semidirect |
| 212. C23×Q8 | Dic79 | semidirect |
| 219. #393 | Dic79 | semidirect |
| 222. C2×#95 | Dic79 | semidirect |
| 232. C22×Q8 | C2×Dic79 | semidirect |
| 257. #95 | C2×Dic79 | semidirect |
| 409. C2 | #23761421 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098330 | 2 |
| C2×#19098287 | 2 |
| #23761421 | 2 |
| C2×#393×C79 | 2 |
| C2×#1351 | 79 |