Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
814 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 267 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. #23765653 | C2 | direct (N × H) |
| 52. C2×C4×C79 | Q32 | semidirect |
| 70. C4×C79 | C2×Q32 | semidirect |
| 75. C2×C79 | #2247 | semidirect |
| 82. C79 | C2×#2247 | semidirect |
| 135. C2×C4 | Dic632 | semidirect |
| 149. C4 | C2×Dic632 | semidirect |
| 152. C2 | #23765653 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic632 | 2 |
| C2×#19098943 | 2 |
| #23765653 | 2 |
| C2×C4×C16×C79 | 2 |
| C2×#2247 | 79 |