Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1110 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1110 conjugacy classes of subgroups — too many to draw. Only its 459 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 |
|---|---|---|
| 8. C4×Dic316 | C4 | direct (N × H) |
| 40. Dic316 | C42 | direct (N × H) |
| 53. C42×C79 | Q16 | semidirect |
| 75. C4×C79 | C4×Q16 | semidirect |
| 89. C79 | C42×Q16 | semidirect |
| 137. C42 | Dic316 | direct (N × H) |
| 161. C4 | C4×Dic316 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic316 | 2 |
| C42×Dic158 | 2 |
| C4×#14579095 | 2 |
| C4×#14579086 | 2 |
| C42×C8×C79 | 2 |
| C42×Q16 | 79 |