Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
11166 conjugacy classes of subgroups; only the 4427 normal subgroups are shown.
This group has 11166 conjugacy classes of subgroups — too many to draw. Only its 4427 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. C23×#11929614 | C2 | direct (N × H) |
| 8. C22×#11929614 | C22 | direct (N × H) |
| 17. C2×#11929614 | C23 | direct (N × H) |
| 28. #11929614 | C24 | direct (N × H) |
| 30. C24×C79 | Q16 | semidirect |
| 37. C23×C79 | C2×Q16 | semidirect |
| 48. C22×C79 | C22×Q16 | semidirect |
| 55. C2×C79 | C23×Q16 | semidirect |
| 61. C79 | C24×Q16 | semidirect |
| 82. C24 | #11929614 | direct (N × H) |
| 94. C23 | C2×#11929614 | direct (N × H) |
| 105. C22 | C22×#11929614 | direct (N × H) |
| 111. C2 | C23×#11929614 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic158 | 2 |
| C23×#11929614 | 2 |
| C24×C79⋊C8 | 2 |
| C24×Q8×C79 | 2 |
| C24×Q16 | 79 |