Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
13310 conjugacy classes of subgroups; only the 8715 normal subgroups are shown.
This group has 13310 conjugacy classes of subgroups — too many to draw. Only its 8715 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 |
|---|---|---|
| 1. C23×#11929608 | C2 | direct (N × H) |
| 2. C24×C79⋊C8 | C2 | semidirect |
| 4. C22×#11929608 | C22 | direct (N × H) |
| 5. C23×C79⋊C8 | C22 | semidirect |
| 11. C2×#11929608 | C23 | direct (N × H) |
| 12. C22×C79⋊C8 | C23 | semidirect |
| 21. #11929608 | C24 | direct (N × H) |
| 22. C2×C79⋊C8 | C24 | semidirect |
| 24. C24×C79 | M16 | semidirect |
| 33. C23×C79 | C2×M16 | semidirect |
| 41. C79⋊C8 | C25 | semidirect |
| 43. C22×C79 | C22×M16 | semidirect |
| 51. C2×C79 | C23×M16 | semidirect |
| 56. C79 | C24×M16 | semidirect |
| 75. C24 | #11929608 | direct (N × H) |
| 86. C23 | C2×#11929608 | direct (N × H) |
| 96. C22 | C22×#11929608 | direct (N × H) |
| 103. C2 | C23×#11929608 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11929608 | 2 |
| C24×C79⋊C8 | 2 |
| C25×C4×C79 | 2 |
| C24×M16 | 79 |