Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
200 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 71 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. #23761599 | C2 | semidirect |
| 4. #23761581 | C2 | semidirect |
| 6. #23761534 | C2 | semidirect |
| 7. C4×Q32×C79 | C2 | semidirect |
| 10. #19098400 | C4 | semidirect |
| 27. C79⋊C32 | C2×C4 | semidirect |
| 31. Q32×C79 | C2×C4 | semidirect |
| 87. C4×Q32 | D79 | semidirect |
| 93. C79 | #13652 | semidirect |
| 111. Q32 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098400 | 2 |
| C4×D1264 | 2 |
| #23761599 | 2 |
| #23761581 | 2 |
| #23761577 | 2 |
| #23761534 | 2 |
| C4×Q32×C79 | 2 |
| #13652 | 79 |