Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
214 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 75 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. C4×D1264 | C2 | semidirect |
| 3. #23761600 | C2 | semidirect |
| 4. #23761579 | C2 | semidirect |
| 5. C4×C32×C79 | C2 | semidirect |
| 8. D2528 | C4 | direct (N × H) |
| 17. D1264 | C2×C4 | semidirect |
| 24. C32×C79 | C2×C4 | semidirect |
| 53. C4×C79 | D32 | semidirect |
| 66. C4×C32 | D79 | semidirect |
| 67. C79 | C4×D32 | semidirect |
| 86. C32 | C4×D79 | semidirect |
| 116. C4 | D2528 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D2528 | 2 |
| C4×D1264 | 2 |
| #23761600 | 2 |
| #23761579 | 2 |
| C4×C32×C79 | 2 |
| C4×D32 | 79 |