Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
194 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23765277 | C2 | semidirect |
| 3. #23761607 | C2 | semidirect |
| 4. #23761589 | C2 | semidirect |
| 5. #23761587 | C2 | semidirect |
| 6. #23761536 | C2 | semidirect |
| 7. C79×#2179 | C2 | semidirect |
| 10. #19098400 | C4 | semidirect |
| 11. #19098398 | C4 | semidirect |
| 28. C79⋊C32 | C2×C4 | semidirect |
| 31. Q32×C79 | C2×C4 | semidirect |
| 33. D16×C79 | C2×C4 | semidirect |
| 89. #2179 | D79 | semidirect |
| 95. C79 | #13658 | semidirect |
| 113. Q32 | C4×D79 | semidirect |
| 117. D16 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765712 | 2 |
| #23765277 | 2 |
| #23761607 | 2 |
| #23761589 | 2 |
| #23761587 | 2 |
| #23761536 | 2 |
| C79×#2179 | 2 |
| #13658 | 79 |